Optical conductivity of iron-based superconductors

According to the predictions of ab initio electronic band-structure calculations, the intermediate-energy electronic band structure (within $\approx \pm 3 \text{eV}$ from the Fermi level) of virtually all iron-based materials is dominated by the more or less hybridized 3d orbitals of iron ions and 4p orbitals of the pnictogen/chalcogen [18]. This suggests that all of these materials should have quite similar overall structure of the interband optical transitions in this energy range even upon substitution. Optical investigations on a large subset of the iron-based compounds have indeed confirmed this conclusion. Figure 3 shows a representative spectrum of the optical conductivity of a hole-doped Ba_0.68K_0.32Fe₂As₂, the theoretical prediction, as well as the corresponding electronic band structure obtained for this material in the local-density approximation [90]. The Drude-Lorentz analysis of the experimental data allows one to clearly identify three main contributions to the interband optical conductivity (red, green, and blue Lorentzians in figure 3(a)). A comparison with the theoretical prediction and the underlying electronic band structure plotted in figures 3(b) and (c) allows one to assign these different contributions to the following transitions:

• the lowest-energy interband contribution (red line in figures 3(a) and (b)) originates in transitions from weakly hybridized Fe-d (red lines in figure 3(c)) and As-p (blue lines in figure 3c) states below the Fermi level to Fe-d states of electronic character in the vicinity of the Fermi level (purple lines in figure 3(c));
• the intermediate-energy interband contribution (green line in figures 3(a) and (b)) stems from transitions from the same initial states to strongly hybridized Fe-d and As-p states above the Fermi level (green lines in figure 3(c));
• finally, the higher-energy contribution (blue line in figures 3(a) and (b)) comes predominantly from transitions from all of the above initial states to Ba-d states above the Fermi level.

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This general structure of the interband optical conductivity is largely independent of the intercalating atom, as demonstrated in [98] and summarized in figure 4.

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It is evident from the comparison in figure 3 that the agreement between between experiment and theory is rather satisfactory in this intermediate energy range except for the significant softening of the 1.5 eV band predicted by ab initio calculations to about 0.6–0.75 eV inferred from experimental data (peak positions of the red lines in figure 3(a) and (b), i.e. by a factor of about 2.5. According to the assignment above, this shift must come predominantly from the bandwidth renormalization of the Fe-d states below the Fermi level (red lines in figure 3(c)). Such a renormalization has been observed consistently in many different iron-based materials using angle-resolved photoemission spectroscopy [22, 33–37]. The experimentally observed location of the absorption band at about 0.6–0.75 eV has been reproduced by theoretical calculations in the dynamic mean-field theory [106, 107], which identified the origin of the aforementioned renormalization in substantial Hund's-coupling correlations between the Fe-d electrons in the iron-based compounds.

The occurrence of numerous Fe-d bands very close to the Fermi level results in the concentration of sizable spectral weight in the mid-infrared optical band at quite low energies. As a result, this absorption band makes an unusually large contribution to the total zero-frequency interband permittivity $\Delta{{\varepsilon}_{\text{tot}}}$ on the order of 60, which leads to a drastic reduction of the plasma frequency of itinerant charge carriers by a factor of ∼8 with respect to its bare value [90, 98, 99].

As already mentioned, all single-phase iron-based materials remain conductive at all attainable temperatures, doping levels and pressures. This implies that the low-energy, far-infrared, optical conductivity can be expected to be dominated by the itinerant-charge-carrier response. Such behavior has indeed been observed in all studied compounds of the iron-based family, as will be shown below. However, unlike in conventional metals, the infrared charge dynamics of these materials was found to have pronounced bad-metal characteristics, exhibiting a long high-frequency tail along with a coherent low-frequency response. This ambivalent response can be modeled with two independent Drudelike contributions to the optical conductivity: a very narrow, 'coherent', and a broad, 'incoherent' term, as first demonstrated in [110] for a representative set of 122 compounds (see figures 5(a)–(e), (g)–(i)) as well as in [111, 112] for Ba(Fe_1-xCo_x)₂As₂ and later found in other classes of the iron-based family [113, 114] and different isostructural compounds (see figures 5(j)–(m)). While the precise properties of the two types of itinerant response to some extent depend on the material composition, the breakdown into a coherent and incoherent contribution is universal. It is, therefore, important to understand the origin of these two types of response and their relation to itinerant charge carriers. The most straightforward explanation would be to remember that all iron-based materials are inherently multiband compounds and thus possess multiple electronic subsystems according to the number of Fermi-surface sheets. In the case of weakly interacting quasiparticles, the width of the free-charge-carrier response would be dominated by the rate of scattering from impurities in the crystal. This argument would then lead one to conclude that there are two types of charge carriers in the system: one that experiences very strong impurity scattering, giving rise to the incoherent part of the itinerant response, while the other is subject to much weaker scattering, thus producing a very narrow, coherent, Drudelike term in the optical conductivity. Since in this case all of the scattering comes from randomly distributed impurities in the crystal, one may extract the quasiparticle mean-free path from the experimentally obtained scattering rate. In iron-based compounds the latter is on the order of 2500 cm⁻¹ [98]. Assuming the Fermi velocity of about 0.4 eV Å⁻¹, one obtains the mean-free path of 0.8 Å, much smaller than the in-plane lattice constant of about 3.7 Å and even smaller than the shortest interionic distance [10]. This situation is clearly unphysical and suggests that the incoherent term might be unrelated to the itinerant response in the iron-based compounds but might instead be a manifestation of low-lying interband transitions, indeed predicted by ab initio calculations [115, 116] and recently identified experimentally [117]. However, the total spectral weight of these low-energy transitions (both in theory and in experiment) is several orders of magnitude smaller than that of the incoherent conductivity term. Moreover, the detailed analysis of the optical spectral weight in Ba(Fe_1-xCo_x)₂As₂ has revealed that only by assigning most of the spectral weight at energies up to 1500 cm⁻¹ to the response of itinerant charge carriers does one find consistency with band-structure renormalization revealed by other probes [118].

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The above difficulty with the unphysically small mean-free path inferred from the very large quasiparticle scattering rate of the incoherent term can be completely resolved if one considers interacting quasiparticles. In this case, the total scattering is a combination of the elastic scattering from impurities in the crystal mentioned above and the inelastic scattering mediated by various bosonic excitation coupled to the itinerant charge carriers (such as phonons, spin fluctuations, orbital fluctuations, etc.) [120, 121]. The inelastic scattering rate is determined by the strength of the electron-boson interaction and is unrelated to the lattice and impurities in the crystal. Good nesting between the hole- and electronlike sheets of the Fermi surface originally identified in the iron-based compounds from ab initio calculations could in principle provide a large enough density of states for the corresponding bosonic excitations to give rise to the observed magnitude of the quasiparticle scattering rate of the incoherent itinerant response. However, as has been mentioned in the introduction, the experimentally determined Fermi surface topology essentially excludes any effective nesting in iron-based compounds. Additionally, the observation of very similar incoherent response in iron-based materials with quite different compositions and, as a result, drastically different Fermi surfaces and types of dominating charge carriers [10, 12] implies that it is unrelated to the specific structure of the Fermi surface but rather is a universal feature in this family of compounds [109]. One of the plausible candidates for the source of the strong interactions underlying the incoherent term in the optical conductivity seems to be Hund's-coupling orbital correlations between Fe-d electrons, predicted to have a sizable intensity and play an important role in the low-energy electrodynamics of the iron-based materials [107]. Recent detailed optical study of several isostructural 122 compounds has revealed the presence of the incoherent term in the optical conductivity of various 3d-transition-metal-based materials, in stark contrast to its complete absence in $\text{CaC}{{\text{u}}_{2}}\text{A}{{\text{s}}_{2}}$ (see figure 5), a 4s metal with a fully filled 3d shell, thus entirely lacking Hund's-coupling correlations. A detailed analysis of the relative intensity of the coherent and incoherent contributions to the optical conductivity as a function of doping has revealed a pronounced dependence of the degree of incoherence on the pnictogen-transition metal-pnictogen bond angle and the electron filling of the transition-metal 3d orbitals (figure 6), both of which provide a measure of electronic correlations. An angle-resolved photoemission spectroscopy study of the fully cobalt-substituted $\text{BaC}{{\text{o}}_{2}}\text{A}{{\text{s}}_{2}}$ has likewise revealed significantly weaker electronic correlations compared to its iron-based counterpart due to the higher filling of the Co-3d orbitals in the presence of strong Hund's-coupling correlations [122]. The degree of electronic correlations can further be assessed by comparing the spectral weight of itinerant charge carriers (related to their kinetic energy [123, 124]) extracted from the optical conductivity obtained experimentally and in ab initio band-structure calculations and has been found to be quite substantial [118]. At the same time, numerous previous studies of the iron-based materials have revealed a trend towards the maximization of the superconducting transition temperature close to the ideal tetrahedral coordination $\left({{\alpha}_{\text{bond}}} \approx {{109.5}^{{}^\circ}}\right)$ of the transition metal and pnictogen ions [10, 58]. It therefore appears that strong electronic correlations are an essential ingredient of high-temperature superconductivity in the iron-based materials. The importance of orbital physics in the iron-based superconductors is further reflected in the correlation between the magnitude of the superconducting energy gap and the orbital character of the Fermi-surface sheets on which it occurs, identified by means of angle-resolved photoemission spectroscopy [39].

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In the case of interacting quasiparticles, the traditional Drude expression for the optical conductivity of itinerant charge carriers can be generalized to the so-called extended Drude model [3]. The complex optical conductivity σ(ω) = σ₁(ω) + iσ₂(ω), determined by two real-valued functions of frequency σ₁(ω) and σ₂(ω), is uniquely expressed in this model in terms of two different functions: frequency-dependent quasiparticle scattering rate γ(ω) and mass renormalization $m\left(\omega \right)/{{m}_{\text{band}}}$, where ${{m}_{\text{band}}}$ is the bare quasiparticle effective mass. Since such a mapping always exists for an arbitrary shape of the optical conductivity, whether it truly represents itinerant-charge-carrier response or not, extreme care must be taken in the interpretation of the results of such a data analysis. As it so happens, several properties of the iron-based materials eloquently highlight the main difficulties of the extended-Drude approach.

The first complication comes from the relatively low-lying intense interband transitions. A typical extended Drude analysis of a correlated material would be confined to the frequencies on the order of the largest quasiparticle scattering rate or less, in the pnictides—usually up to around 1000–2500 cm⁻¹. As was discussed above, the lowest-energy pronounced optical absorption band is located around 0.6–0.75 eV ≈5000–6000 cm⁻¹, i.e. well beyond the frequency range of interest for the extended Drude analysis and thus of little concern. However, this analysis essentially depends not only on the real part of the optical conductivity but also on its imaginary part. While the influence of the 0.6 eV band on the former is negligible, on the latter it is substantial in spite of the fact that it lies well beyond the spectral range of interest, because it makes a very large contribution to the total zero-frequency interband permittivity, on the order of 60. The importance of the constant contribution of each interband transition to the real part of the dielectric function (or, equivalently, to the imaginary part of the optical conductivity: ε(ω) = 1 + 4π iσ(ω)/ω), well below the resonance frequency of that transition, is often forgotten because in the overwhelming majority of materials this contribution is very small, adding up to a value of order unity. The iron-based compounds are one of the prominent exceptions. Figure 7 demonstrates the effect of unsubtracted interband transitions above 0.6 eV on the extended Drude analysis below 1000 cm⁻¹ in the low-temperature normal state of superconducting Ba_0.68K_0.32Fe₂As₂. It is clear that, with all interband transitions eliminated, the quasiparticle scattering rate saturates above 300 cm⁻¹. In contrast, if the extended Drude analysis is carried out on the raw data then the quasiparticle scattering rate shows a linear increase up to very high frequencies, albeit such a linear frequency dependence is a mere artifact of the data analysis and can be mistaken for the signatures of strong electronic correlations or a quantum critical point [99, 115, 125]. In light of the recently reported observation of low-energy absorption bands around 1000 cm⁻¹ and 2300 cm⁻¹ in Ba(Fe_1-xCo_x)₂As₂ (albeit of rather low intensity) [117] in line with the theoretical predictions [115, 116] even more care should be exercised in order not to misinterpret the extrinsic effect of interband transition as intrinsic properties of itinerant charge carriers.

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The second complication in the extended-Drude analysis of the optical conductivity of the iron-based materials comes from the inherently multiband character of the latter, as this implies the existence of multiple electronic subsystems, each with its own quasiparticle properties. In the case of a single-band material with weakly interacting quasiparticles, the extended Drude analysis of the optical conductivity provides a physically correct result: constant quasiparticle scattering rate equal to the elastic scattering rate from random impurities in the crystal, as well as unity effective-mass renormalization. In the multiband case, however, even if the quasiparticles in all of the bands are weakly interacting, a simple application of the extended Drude analysis to the total optical conductivity of all bands will result in a frequency-dependent quasiparticle scattering rate and effective-mass renormalization. Even though the procedure is mathematically correct and the result is unique, its interpretation is difficult, unless all bands have very similar properties, which is not the case for the iron-based compounds. If, in addition, every band features (strongly) interacting quasiparticles, the rationality of this analysis appears dubious.

It is, therefore, more reliable to start with a certain microscopic model of the normal-state multiband optical conductivity, such as the Eliashberg theory [2], constrained by a large body of experimental data obtained with other techniques and fit the frequency-dependent quasiparticle scattering rate and effective-mass renormalization obtained in this model to those extracted via the effective Drude analysis of the experimental optical conductivity data [99]. In this approach the interpretation of the latter is irrelevant and it is used as a sheer mathematical transformation of the original complex optical conductivity, which might provide certain insights into some characteristics of the underlying physical phenomena. If, on the other hand, the multiband extended-Drude data are fitted or inverted in a single-band theory one might still be able to get approximate qualitative information about the energy scales of relevant interactions [127]. However, there is a significant risk of mistaking multiband effects for intrinsic properties of quasiparticle interactions.

Upon lowering the temperature, essentially all of the iron-based compounds undergo a sequence of a structural and a magnetic phase transition [10, 12]. At the structural transition the C4 rotational symmetry of the tetragonal high-temperature state is reduced to the orthorhombic C2 symmetry in a weakly or strongly first-order phase transition [128], with the new orthorhombic crystallographic axes rotated by 45° with respect to their tetragonal counterparts. This process is accompanied by the formation of twin domains, oriented perpendicularly to each other due to the two possible directions for the longer orthorhombic axis. At a somewhat lower temperature the materials enter an antiferromagnetically ordered phase that exhibits a finite magnetic moment on iron ions and a corresponding reconstruction of the Brillouin zone [129] but retains metallic properties. The latter, together with the early observation of a relatively small ordered moment, suggested that the antiferromagnetic state in the iron-based materials is of itinerant character and thus is driven by the nesting instability of the Fermi surface at a commensurate nesting vector connecting the hole and the electron sheets of the Fermi surface predicted by ab initio calculations [18]. However, as already mentioned above, extensive ARPES [32] and neutron-scattering [23] investigations of various iron-based materials have identified virtually absent nesting and an essentially dual, simultaneously itinerant and local, character of antiferromagnetism in these compounds, respectively.

The low-energy modification of the electronic band structure induced by the antiferromagnetic phase transition can be probed effectively by studying its effect on the charge dynamics reflected in the optical conductivity. Even very early investigations of the latter in many different iron-based parent compounds revealed a strong suppression of the infrared conductivity at the Néel temperature below a certain energy [55, 110–112, 126, 130–133]; see figure 8. Due to the conservation of the total number of electrons, the missing area under the conductivity curve below this energy is transferred to higher energies, which results in the formation of a 'hump' structure [134, 135]. In the case of itinerant magnetism the above suppression in the optical conductivity results from the opening of the so-called spin-density-wave energy gap at the hot spots of the Fermi surface (portions of the Fermi surface connected by the nesting vector). In the most common case of imperfect nesting the hot spots and, consequently, the spin-density-wave gap do not cover the entire Fermi surface. Therefore, the material remains metallic in the low-symmetry state, with the optical conductivity non-zero at all frequencies. This circumstance makes the determination of the optical spin-density-wave energy gap $2{{\Delta}_{\text{SDW}}}$ from the conductivity spectra difficult but it can be approximated by the energy at which the low-temperature conductivity spectrum crosses the one at the Néel temperature for the first time [135]. Having estimated the energy gap one may proceed to calculate the corresponding gap ratio $2{{\Delta}_{\text{SDW}}}/{{k}_{\text{B}}}{{T}_{\text{N}}}$, i.e. the ratio of the optical energy gap $2{{\Delta}_{\text{SDW}}}$ and the Néel temperature in energy units ${{k}_{\text{B}}}{{T}_{\text{N}}}$, where ${{k}_{\text{B}}}$ is the Boltzmann constant. The gap ratio provides a rough estimate of the coupling strength between electrons giving rise to a given electronic instability, such as superconductivity, spin-density-wave etc. [2, 136]. A systematic comparison of the gap ratios of three common ThCr₂Si₂-type iron-based parent compounds was given in [98]. This study found a clear trend towards stronger coupling with decreasing atomic number of the intercalating atom: from barium via strontium to calcium. A similar trend was found in the total plasma frequency of the itinerant charge carriers, with CaFe₂As₂ being significantly more metallic than the other two materials.

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As can be seen in figure 8, the optical conductivity of BaFe₂As₂ and SrFe₂As₂ reveal a change in shape at lowest frequencies at 10 K as compared to intermediate temperatures below ${{T}_{\text{N}}}$, which indicates the presence of another spin-density-wave gap, with a smaller magnitude. This feature has also been observed in BaFe₂As₂ and CaFe₂As₂ compounds in [118] and [98], respectively, and associated with a second spin-density-wave energy gap. The existence of two separate spin-density-wave energy gaps raises a question as to the degree of interaction between the corresponding electronic subsystems. This question becomes particularly difficult to address in the presence of as many Fermi-surface sheets as is the case in the iron-based materials, which commonly possess up to five separate Fermi-surface sheets in the first Brillouin zone. This complexity arises mainly due to the fact that the optical conductivity represents an intertwined response of all electronic subsystems at once. To shed some light onto this issue detailed measurements in the far-infrared spectral range (i.e. in the range where the real part of the optical conductivity experiences a drastic suppression, as shown in figure 8) on a very fine temperature grid were carried out for three 122 parent materials in [98]. The results are compiled in figure 9, which shows the temperature dependence of the optical conductivity normalized to its value at $T={{T}_{\text{0}}}$ close to ${{T}_{\text{N}}}$ (T₀ = 170 K, 200 K, and 140 K for the Ca-, Sr-, and Ba-based compounds, respectively) at an equidistant set of wavenumbers from 180 cm⁻¹ (blue colors) to 520 cm⁻¹ (red colors) in steps of 20 cm⁻¹ with the exception of the spectral window of the 260 cm⁻¹ phonon for the Ca- and Sr-based compounds, as well as from 220 cm⁻¹ to 580 cm⁻¹ for $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$.

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The temperature dependence of the normalized conductivity shows a very pronounced drop for all compounds at their respective Néel temperatures (right vertical dashed lines) due to the onset of spin-density-wave order, with a clear mean-field order-parameter-like temperature dependence at large wavenumbers (red colors). This temperature dependence changes, however, as one moves toward progressively smaller wavenumbers and in the case of $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ reveals a clear second suppression feature at a temperature T^* of about 80 K. This second feature becomes washed out in the Sr-based compound, although the temperature dependence of σ₁ at the smallest wavenumbers remains markedly different from that at large wavenumbers and some sort of an analogue of T^* can be sketched also in this case, although there is no clear second suppression feature present in any of the separate temperature dependences themselves. Finally, in the case of $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, the change in the temperature dependence of σ₁ between large and small wavenumbers becomes hardly noticeable, with the exception of an upturn in its temperature dependence at intermediate frequencies due to the pile-up of the spectral weight transferred from the energies below the smaller spin-density-wave energy gap.

The presence of the second suppression feature in the temperature dependence of the real part of the optical conductivity at small enough wavenumbers in $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ indicates that the electronic subsystem that develops the smaller spin-density-wave energy gap $2\Delta_{\text{S}}^{\text{SDW}}$ preserves some knowledge about its own Néel temperature that it would have if this subsystem were completely independent from the other(s). In any real material all electronic subsystems are coupled, even if weakly, so that all spin-density-wave energy gaps open at the same ${{T}_{\text{N}}}$. However, in case of weak intersubsystem coupling, those with smaller gaps exhibit an anomaly below the real Néel temperature, as is the case in $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, albeit this anomaly does not correspond to a true phase transition. Such an effect has been predicted theoretically for the analogous case of multiband superconductivity [137, 138] and discovered experimentally in $\text{FeS}{{\text{e}}_{1-x}}$ in [139–141]. The corresponding non-BCS temperature dependence of the smaller superconducting gap resulting from weak interband coupling seems to be consistent with the scanning tunneling spectroscopy data obtained on the LiFeAs compound [142].

This argument thus suggests that in the Ca-based material the two electronic subsystems developing the large and the small spin-density-wave energy gap are weakly coupled. Naturally, as the coupling between such electronic subsystems increases, the temperature dependence of the small gap would gradually approach that of the large gap via an intermediate state when it already does not show any anomaly but still has not matched the temperature dependence of the large gap. Figure 9(b) provides evidence for such a behavior in the Sr-based iron pnictide. Finally, the temperature dependence of the normalized optical conductivity in $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ is almost the same at all wavenumbers, both in the region of the large spin-density-wave gap and in that of the small one, indicating strongly coupled electronic subsystems in this compound. Thus, by monitoring the detailed temperature dependence of the optical conductivity in the far-infrared spectral range on a fine grid of wavenumbers, a gradual transition could be observed from weak coupling between the electronic subsystems developing the two different spin-density-wave energy gaps in $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, via intermediate coupling in $\text{SrF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, to strong coupling between them in $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, systematically with increasing atomic number of the intercalant.

We have consistently emphasized throughout this review that, albeit originally believed to be purely itinerant, the antiferromagnetism of the iron-based compounds has been found to bear essentially dual, itinerant and local character [23]. This suggests that the spectral-weight redistribution found in the optical conductivity of antiferromagnetic compounds might be driven by local-moment physics as well as by the opening of a spin-density-wave energy gap due to collective long-range order. This idea has indeed received significant attention. For instance, the authors of [130] have assigned the smaller and the larger gaplike features in EuFe₂As₂, similar to those discussed above, to two different sets of optical transitions: related to transitions within the spin-minority bands formed by Fe ions with the same spin and, therefore, sensitive to the long-range magnetic order and between the spin-majority and the spin-minority bands formed by Fe sites with opposite spins, respectively. The latter is mostly defined by the exchange splitting of the local magnetic moment due to Hund's coupling and thus is less sensitive to the long-range order. Calculations taking into account electronic correlations based on a combination of the density-functional and dynamic-mean-field theory have likewise emphasized that it is the gain of Hunds-coupling energy rather than Hubbard repulsion energy that compensates for the loss in kinetic energy and thus stabilizes the low-temperature antiferromagnetic phase [107]. The same study has achieved a remarkable agreement in the overall shape between the calculated and experimentally obtained infrared conductivity of BaFe₂As₂ in the antiferromagnetic ground state, albeit with a substantially overestimated electronic background [118].

Theoretical calculations in both [130] and [107] have shown that the significant role played by Hund's coupling in the magnetism of the iron-based compounds leads to a modification of the electronic band structure on the energy scale of several electron-volts in the antiferromagnetic ground state compared to the high-temperature paramagnetic state. A detailed ellipsometric study of the SrFe₂As₂ compound [90] and its subsequent systematic comparison to the CaFe₂As₂ and BaFe₂As₂ compounds [98] have revealed that energies even higher than expected, on the order of 4–5 eV, are in fact affected by the antiferromagnetic phase transition, as shown in figure 10. The optical conductivity of all three compounds experiences a drastic suppression upon entering the antiferromagnetic state (figures 10(a)–(c)). The magnetism-induced character of these modifications is confirmed by a sharp drop at the Néel temperature observed in the temperature dependence of the imaginary part of the dielectric function shown in the insets of figures 10(d) and (f) as well as in [98]. The magnitude of the suppression decreases systematically from the Ca- via the Sr- to the Ba-based compound, roughly proportionally to the square of the gap ratio determined from infrared-conductivity measurements on the same compounds [98]. Quite surprisingly, a similar although much smaller suppression has also been found to occur at the superconducting transition temperature in the non-magnetic Ba_0.68K_0.32Fe₂As₂ compound at optimal doping level [90]. This discovery has suggested that the suppression likely results from a redistribution of the electronic population at the superconducting transition between several electronic bands.

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Additional information about the energy scales involved in the antiferromagnetic phase transition in CaFe₂As₂, SrFe₂As₂, and BaFe₂As₂ can be inferred from a detailed analysis of the spectral-weight transfer in the optical conductivity at across the Néel temperature (see figures 10(d)–(f)). Several common features can be identified in the energetics of the spin-density-wave transition: the spectral weight from below the optical spin-density-wave gap $2{{\Delta}^{\text{SDW}}}$ (lowest-energy red area in figure 10(e) and the corresponding areas in figures 10(d) and (f) is redistributed to energies directly above the optical gap (subsequent blue area in figure 10(e) and the corresponding areas in figures 10(d) and (f). However, the spectral weight gained directly above the optical gap does not balance that lost within the gap, which implies that higher-energy processes beyond the characteristic magnetic energy scales proposed for the iron-based compounds are affected by the spin-density-wave transition, as discussed above, including the spin-density-wave-suppressed band in the visible spectral range (higher-energy blue and red areas in figure 10(e) and the corresponding areas in figures 10(d) and (f).

In contrast to the case of the phase transition, the temperature-induced spectral-weight transfer above the Néel temperature in $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ (red solid line in figure 10(d)) leaves the low-energy itinerant-charge-carrier response largely unaffected and is dominated by the temperature dependence of the 0.6 eV absorption band, ubiquitous in the iron-based materials, as can be seen in figure 4. The compensating effect due to the suppression of the 3.5 eV absorption band is entirely absent in the normal state and only a very weak decrease in the spectral weight at higher energies takes place, comparable to that across the spin-density-wave transition. The absence of any significant temperature dependence of the 3.5 eV absorption band above ${{T}_{\text{N}}}$ is further confirmed by the temperature scan of the imaginary part of the dielectric function at 3.5 eV shown in the inset of figure 10(d).

The general features of the infrared- and Raman-active phonons allowed by the tetragonal symmetry of the iron-based compounds and observed experimentally have been discussed in detail in [133]. Therefore, here we will concentrate on the phonon anomalies induced by the antiferromagnetically ordered phase.

The lowering of the crystal symmetry at the virtually simultaneous structural and antiferromagnetic phase transition in the ThCr₂Si₂-type iron-based parent compounds must result in the splitting of the two in-plane infrared-active phonon modes of the high-temperature tetragonal phase [133, 144] and this has indeed been observed [98, 143]. While the splitting of the lower-energy phonon mode involving the intercalating ion can be seen very clearly in the optical conductivity of the parent BaFe₂As₂ compound (figure 11(a)), that of the higher-energy Fe-As vibrational mode is anomalous and features an extreme asymmetry in the intensity of the two split branches, with one of them being hardly distinguishable over the noise floor, as shown in figure 11(b). Very careful infrared reflectance measurements reported in [143] and shown in figure 11 allowed one to distinguish all in-plane infrared-active phonon modes and trace their splitting upon entering the low-temperature orthorhombic phase. These measurements suggested that the large asymmetry as well as the unusual temperature dependence of the phonon intensities below the Néel temperature can only be explained by assuming a highly anisotropic electronic state in the antiferromagnetic phase due to strong Hund's-coupling correlations predicted theoretically [107], which would result in a different electronic background and thus screening of ionic vibrations by itinerant charge carries along the direction of the ferro- and antiferromagnetically ordered magnetic moments. This conclusion has been directly confirmed by the polarization-dependent measurements of the optical conductivity of mechanically detwinned Ba(Fe_1-xCo_x)₂As₂ samples, reviewed in the next section.

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A very detailed study of the temperature dependence of the intensity, position, and width of the infrared-active phonons of CaFe₂As₂, SrFe₂As₂, and BaFe₂As₂ compounds and their comparison has been reported in [98] and is presented in figure 12. The low-energy phonon due to the vibrations of the intercalating ions is reported only for the Ca-based parent compound (located at ≈140 cm⁻¹) but not in the Sr- and Ba-based counterparts because for the latter it is located outside the experimentally accessible spectral range. The phonon arising from vibrations of Fe and As is seen at approximately the same position of 260 cm⁻¹ in all three materials. In the $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ compound, the splitting of the Ca-related phonon at the magnetostructural transition can be clearly resolved and amounts to about 8 cm⁻¹ (figure 12(b)). Within the noise floor the temperature dependence of the width of these two phonons, plotted in figure 12(c), does not appear to display any anomalies. That of the phonon strength Δε, on the other hand, seems to slightly change at the temperature T^* (left vertical dashed line in 12(a)) inferred from figure 9(a), albeit this change is quite close to the limit of the fit uncertainty.

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The temperature dependence of all Lorentz parameters of the Fe-As phonon in all three compounds, figures 12(d)–(f), shows noticeable anomalies at the respective Néel temperatures (grey, light blue, and pink vertical dashed lines for Ca-, Sr-, and Ba-based compounds, respectively). In $\text{SrF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ and $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ the phonon intensity Δε₀ and position ω₀ change abruptly at the magnetostructural transition temperature, as shown in figures 12(d) and (e), whereas in $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, quite surprisingly, the spin-density-wave-induced changes seem to set in already at somewhat higher temperatures (figure 12(e)). This observation indicates the existence of incipient critical lattice strain at temperatures higher than the magnetostructural transition temperature in this compound, which may be related to the electronic nematicity recently discovered in a doped compound of this class [145] and reviewed in more detail in the next section. In addition, while the width and the position of the Fe-As phonon in both Sr- and Ba-doped compounds (figures 12(e) and (f) display essentially identical magnitude and behavior, those of the Ca-doped material are significantly larger. While the somewhat broader phonon feature could, in principle, be traced back to the quality of the sample surface or the sample itself, the harder Fe-As phonon of Ca-based compound compared to its Sr- and Ba-based counterparts must be intrinsic. Such a hardening most likely results from the shorter Ca-As and Fe-As bond lengths compared to those in the Sr- and Ba-based compounds and has also been observed in inelastic-neutron-scattering measurements on $\text{CaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$, $\text{BaF}{{\text{e}}_{2}}\text{A}{{\text{s}}_{2}}$ and predicted by ab initio calculations [146].

Very early theoretical investigations of the electronic band structure of the iron-based compounds predicted a strongly anisotropic electronic state in the low-temperature antiferromagnetic phase due to the importance of Hund's-coupling correlations [107]. Experimentally, however, this issue had received limited attention until the discovery of a pronounced anisotropy in the dc resistivity of detwinned underdoped Ba(Fe_1-xCo_x)₂As₂ compounds significantly above the Néel transition temperature [83]. This observation has led to an explosion of research into the electronic anisotropy of the antiferromagnetic ground state and the symmetry-breaking fluctuations which lead to the occurrence of anisotropy in the high-temperature tetragonal phase above the magnetostructural transition upon application of detwinning pressure/strain, reviewed in this section.

The breaking of the fourfold rotational symmetry of the high-temperature tetragonal state at the magnetostructural transition leads to the formation of domains with mutually orthogonal orientation of the now inequivalent in-plane crystallographic axes. Any experimental technique that probes several such domains at once will only be able to access an average of the inherent electronic response in the two inequivalent directions, producing an essentially isotropic result irrespective of the in-plane orientation. In order to overcome this difficulty, the formation of the antiferromagnetic domains must be hindered by imposing a preferred direction in the tetragonal phase through the application of stress or strain. This procedure is fraught with several potential difficulties. First of all, the application of strain/stress by itself breaks the fourfold rotational symmetry of the high-temperature tetragonal phase and thus all measurements carried out on the resulting detwinned samples will not probe the inherent anisotropic electronic response but rather introduce pressure-related effects. Therefore, strain/stress must be released before any measurements are carried out on the detwinned samples. This requirement presents an additional complication for many techniques because of the low Néel transition temperatures of the iron-based compounds. Secondly, if too much strain/stress is applied to the sample, irreversible changes might occur, which would permanently alter the properties of the material. It has also been found that annealing drastically reduces the resistivity anisotropy in Ba(Fe_1-xCo_x)₂As₂ and makes the low-temperature in-plane charge transport of undoped BaFe₂As₂ essentially isotropic [147, 148], see figure 13(a).

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To confirm the intrinsic character of their results and to prove that the observed resistive anisotropy is electronic and not driven by the structural transition enhanced by applied strain, the authors of [83] have designed and successfully implemented a fully electrically controlled detwinning device based on a piezo stage with an additional reference piezo attached to the top surface of the sample. This device enables easy application and removal of strain in a controlled fashion and thus allows one to avoid irreversible damage to the sample as well as completely remove any residual strain [84]. Armed with this elaborate device the authors have revisited their original study and discovered the divergence of the nematic susceptibility under constant strain, i.e. the sensitivity of the electronic anisotropy to the applied stress, which indicates the existence of inherently anisotropic fluctuations in the Ba(Fe_1-xCo_x)₂As₂ material. The authors further found that these fluctuations appear strongest near the optimal doping in this compound, where the long-range antiferromagnetic order disappears and the superconducting transition temperature is the highest, which strongly suggests the existence of a quantum critical point beneath the superconducting dome in these compounds.

A different method to avoid averaging of the anisotropic signal due to the existence of twin domains is to use a sample with the dimensions on the order of the size of a single domain, which will create a natural imbalance of domains with a certain orientation in some samples and thus give an overall anisotropic signal. This approach was used in the thermodynamic study of [85], which observed a finite anisotropy in the magnetic-torque oscillations above the magnetostructural transition in micron-sized BaFe₂(As_1-xP_x)₂ samples.

While the existence of nematic fluctuations in various iron-based compounds has been reliably established, their nature remains unclear. They might originate in the anisotropy of the relative orientation of neighboring spins (anisotropic spin fluctuations) or in the occupation imbalance of the iron ${{d}_{\text{xz}}}$ and ${{d}_{\text{yz}}}$ orbitals (anisotropic orbital fluctuations) [86]. The former scenario is supported by the observation of a clear scaling relation between nuclear-magnetic-resonance and shear-modulus data, probing magnetic and orthorhombic fluctuations, respectively [86, 150]. On the other hand, a sizable orbital anisotropy has recently been discovered by means of x-ray linear dichroism absorption spectroscopy [87] and angle-resolved photoemission spectroscopy [151] on detwinned Ba(Fe_1-xCo_x)₂As₂ samples. This ambivalence indicates an intimate relationship between the spin and orbital degrees of freedom in the iron-based materials [152, 153].

Polarization-dependent measurements of the optical conductivity on mechanically detwinned ThCr₂Si₂-type samples have also revealed a strong anisotropy of the electronic state in the antiferromagnetic phase [132, 149, 154], which persists up to unusually high energies on the order of several electron-volts [154]. Figures 13(b)–(g) show the infrared conductivity of BaFe₂As₂ along the two perpendicular in-plane directions in the low-temperature orthorhombic phase and its evolution upon gradual substitution of cobalt for iron. These polarized infrared measurements, similarly to the unpolarized measurements discussed in the previous sections, reveal the existence of two spin-density-wave-induced gaplike features in the infrared conductivity of the parent BaFe₂As₂ compound along both orthorhombic directions, thus strongly suggesting that the difference in the energy scale of these gaplike features is unrelated to the anisotropy of the magnetic interactions. These measurements further find a coherent and an incoherent contribution to the infrared conductivity along both directions at all investigated doping levels [132, 149, 154].

Given that in the underdoped regime the residual dc resistivity of Ba(Fe_1-xCo_x)₂As₂ samples is dominated by the coherent component (see figure 13), it is instructive to compare their respective anisotropies as a function of cobalt concentration. A detailed analysis reveals that the doping dependence of the anisotropy of both the residual dc resistivity and the quasiparticle scattering rate of the coherent term in the optical conductivity is linear up to the doping level of x = 0.04 and shows a pronouced anisotropy, whereas the spectral weight of the coherent term is isotropic and only weakly depends on the cobalt concentration [148, 149]. This result implies that the anisotropy of the dc resistivity in the antiferromagnetic phase is extrinsic and is likely driven by the anisotropic impurity potential of randomly distributed cobalt dopants [148, 149], polarized by the anisotropic antiferromagnetic environment [155]. Such anisotropic impurity states have indeed been directly visualized by means of scatting tunneling spectroscopy in a related isostructural Ca(Fe_1-xCo_x)₂As₂ system [145].

The doping level of x = 0.04 represents a clear turning point in the doping dependence of the dc-resistivity anisotropy: below this level the latter increases with cobalt concentration and decreases above it [83, 148]. The very same doping level seems to be singular also in the doping dependence of the incoherent contribution to the infrared conductivity, which becomes isotropic by x = 0.04 and virtually ceases to be affected by the antiferromagnetic phase transition. It is noteworthy that this doping level is very close to the zero-temperature boundary of the superconducting region of the phase diagram [83]. The decrease of the anisotropy of the residual dc resistivity beyond the doping level of x = 0.04 is consistent with the weakening of the orthorhombic antiferromagnetic phase and the splitting of the iron ${{d}_{\text{xz}}}$ and ${{d}_{\text{yz}}}$ orbitals [151] in the absence of external pressure towards the doping level at which the structural and Néel temperatures reduce to zero. It is, however, worth noting that a recent study of the linear dichroism in the x-ray absorption of the same Ba(Fe_1-xCo_x)₂As₂ family of compounds has revealed the existence of anisotropic orbital fluctuations stabilized to long-range orbital order under applied pressure well beyond this doping level (at least up to 10%) [87]. Additionally, the divergence of the nematic susceptibility mentioned above was found to be strongly enhanced towards the doping level of x = 0.08, at which the long-range antiferromagnetic order disappears [84].

Detailed transport measurements on Ba(Fe_1-xCo_x)₂As₂, Ba(Fe_1-xNi_x)₂As₂, and Ba(Fe_1-xCu_x)₂As₂ have attributed the nonmonotonic behavior of the anisotropy of the residual dc resistivity with a peak at 4% cobalt doping and its virtual absence in the parent BaFe₂As₂ compound to the existence of a very mobile isotropic subsystem of itinerant charge carriers at zero doping, quickly suppressed upon substitution, thus revealing the underlying anisotropy in the transport of the remaining charge carriers, significant even in the parent compound [156]. This interpretation is consistent with the spectroscopic observation of several contributions to the coherent component of the optical conductivity in BaFe₂As₂, one of which was found to be extremely narrow; it was suggested that it originated in the topologically protected from backscattering sheet of the Fermi surface formed by bands with a Dirac-cone-shape dispersion [154].

The cobalt concentration of 4% also marks the reversal in the spin-density-wave-induced modification of the dc resistivity, which goes from experiencing a suppression at the Néel temperature below this doping level to being enhanced at higher doping levels, as can be clearly seen in figure 13(a) for both directions. This behavior can be easily explained with the help of the spectroscopic data in figures 13(b)–(g). To understand the origin of this phenomenon one needs to remember that the suppression/enhancement of the dc resistivity $({{\rho}_{0}}=4\pi \gamma /\omega _{\text{pl}}^{2}\sim \gamma /n$, where γ is the total elastic scattering rate, ${{\omega}_{\text{pl}}}$ is the plasma frequency of itinerant charge carriers, and n is the electron density) at a spin-density-wave transition is governed by two competing effects, both due to the partial gapping of the Fermi surface: a decrease in the quasiparticle density, which increases the dc resistivity, and a reduction of the quasiparticle scattering rate due to the elimination of some scattering channels, which decreases the dc resistivity. It is quite clear from figure 13(a) that at low doping levels the latter effect dominates and the dc resistivity is significantly reduced below the Néel temperature. The corresponding reduction of the quasiparticle scattering rate below the antiferromagnetic transition can be clearly seen in the spectroscopic data in figures 13(b) and (c). The aforementioned reversal of the suppression in figure 13(a) can now be explained by the gradual decrease in the intensity of the reduction of the quasiparticle scattering rate at the phase transition upon cobalt doping so that at x = 0.04 the two factors in the dc resistivity are comparable and at higher doping levels the decrease in the quasiparticle density starts to dominate and the dc resistivity is enhanced below the Néel temperature. The assumption that the gapping of the Fermi surface below the spin-density-wave transition temperature indeed changes significantly from x = 0 to x = 0.04 is further confirmed by the dramatic reduction of the overall suppression in the optical conductivity with increasing cobalt concentration: at x = 0.04 not only does the quasiparticle scattering rate not show a significant reduction but the overall temperature dependence of the infrared conductivity is rather weak (see figures 13(f) and (g) as compared to that at x = 0 (figures 13(b) and (c).

The infrared phonon due to the relative in-plane displacement of Fe and As ions located at about 260 cm⁻¹ and discussed in the previous section also shows a pronounced anisotropy in the conductivity spectra along the two perpendicular directions in the antiferromagnetic state. Its intensity in the direction of antiferromagnetically ordered ion magnetic moments $\left[{{\sigma}_{\text{b}}}\left(\omega \right)\right]$ is strongly enhanced compared with the high-temperature paramagnetic tetragonal phase, whereas that along the ferromagnetic axis $\left[{{\sigma}_{\text{a}}}\left(\omega \right)\right]$ reduces almost to the noise level, consistent with the previous observations in twinned single crystals [143]. One of the possible explanations for this behavior is the difference in the degree of electronic screening of ionic vibrations in the ferro- and antiferromagnetic directions due to the anisotropic optical conductivity originating in significant Hund's coupling and has been outlined in the previous section. The authors of [149] put forward an alternative explanation suggesting that this lattice vibration produces anisotropic electronic polarization in the antiferromagnetic state, which almost completely cancels out the dipolar field due to the in-plane displacement of Fe and As ions in the ferromagnetic direction and simultaneously enhances it in the perpendicular direction. This anisotropy of the phonon intensity, most pronounced in the parent BaFe₂As₂ compound [149, 154], gradually decreases upon cobalt substitution, which provides additional evidence that the electronic state in the antiferromagnetic phase becomes progressively less polarizable towards the optimal doping level.

Finally, we would like to note that the 0.6 eV absorption band, discussed in detail above and renormalized by strong Hund's-coupling correlations [107], exhibits a pronounced anisotropy in its temperature dependence in the antiferromagnetic state, as can be seen in figures 13(b)–(g).

Superconductivity in the iron-based materials is achieved, in most cases, by iso- or aliovalent substitution into or application of external pressure to the parent antiferromagnetic compounds [10–12]. The superconducting phase occurs once the antiferromagnetic correlations have been sufficiently weakened by one of the aforementioned means and the superconducting transition temperature appears to be maximized at the doping level at which long-range antiferromagnetic order completely disappears and thus the corresponding fluctuations of the iron magnetic moments are the largest. This quite general observation suggests that the exchange of antiferromagnetic spin fluctuations between electrons might mediate their binding into Cooper pairs, similarly to the scenario proposed for the mechanism of superconducting pairing in the copper-based high-temperature superconductors [125]. This conclusion was supported indirectly by the early ab-initio calculations, which demonstrated that the attractive electron-phonon interaction, responsible for the formation of the superconducting state in all conventional superconductors [2], is too weak in the iron-based compounds to be able to account for their relatively high superconducting transition temperatures [24–26]. Since the interaction due to the exchange of antiferromagnetic spin fluctuations is repulsive, the general form of the gap equation [68] maintains that the formation of Cooper pairs can only take place if the superconducting order parameter has opposite signs on different portions of the Fermi surface, in stark contrast to the sign-constant superconducting order parameter in all conventional superconductors [157]. One of the clear manifestations of such an unconventional electronic state is the existence of a resonance peak in the energy spectrum of neutron scattering intensity at the wave vector connecting the portions of the Fermi surface with the opposite signs of the superconducting order parameter [68, 158]. This resonance peak has indeed been observed in virtually all known iron-based superconductors [11].

In the presence of only one large sheet of the Fermi surface, the alternating-sign character of the superconducting order parameter implies the existence of nodes, i.e. zeros in the superconducting energy gap, as is the case in the d-wave copper-based superconductors [159]. The inherently multiband nature of the iron-based materials, on the other hand, makes a realization of nodeless sign alternation across the Fermi surface possible: the so-called extended s-wave or s_± symmetry [18], which complies with the tetragonal symmetry of the underlying lattice, features a different sign of the superconducting order parameter on different sheets of the Fermi surface but requires no nodes. Given that the superconducting energy gap has been found to be nodeless in the majority of the iron-based compounds [10, 160, 161], it is now widely believed that this extended s-wave symmetry is indeed realized in most of the iron-based superconductors, albeit several alternative scenarios have been proposed [42, 44, 45, 162]. Due to the preservation of the tetragonal symmetry of the lattice, a simple phase-sensitive test similar to the one devised to experimentally establish the d-wave symmetry of the order parameter in the cuprate superconductors [28] cannot be carried out. Nevertheless, several ingenious proposals for the determination of the pairing symmetry in the iron-based compounds based on the multiband semimetallic character of these materials have been put forward [29, 30] and even carried out on one member of the iron-chalcogenide family [31].

Superconductivity is an electronic instability of the entire Fermi surface, which implies that all quasiparticle excitations are gapped in the superconducting ground state with the exception of the nodal regions, if any. In the case of the iron-based superconductors it amounts to the presence of as many superconducting energy gaps as there are sheets of the Fermi surface of either electronic character. In all materials on which reliable angle-resolved photoemission measurements have been carried out to date, the existence of up to five superconducting energy gaps has indeed been identified [10, 160, 161]. Quite surprisingly, the specifics of the individual band structure of each particular material notwithstanding, all superconducting gaps have been found to cluster in two groups with approximately the same magnitude (but possibly different signs) within each group but very disparate between them [167]. Such clustering has been observed with a variety of experimental probes [10–12] but its origin remains unclear. It appears likely that orbital-specific interactions might play a key role in this phenomenon.

The clustering of the superconducting energy gaps suggests that it may be possible to distill the essence of the complex multiband (up to five bands) electronic structure of the iron-based superconductors into an effective two-band model by identifying the most important electronic degrees of freedom in these materials. Such efforts have indeed borne some fruit: it has recently been argued that the iron-isospin effective model is able to capture essential low-energy physics [168–170]. Similarly, the analysis of the optical conductivity of a prototypical iron-based superconductor in the framework of the Eliashberg theory has shown that a good semi-quantitative description of the experimental data can be achieved in an effective two-band model [99], obtained via a controlled reduction from a microscopically more accurate four-band model constrained by the aforementioned clustering of the superconducting energy gaps.

The opening of a superconducting gap dramatically affects the low-energy electrodynamics of solids: quasiparticle excitations become eliminated within the energy window of approximately one gap value above and below the Fermi level in all nodeless regions of the Fermi surface. This effect can be clearly identified in the frequency dependence of the complex optical conductivity: due to the conservation of the total number of electrons, the total spectral weight (the area under the real part of the optical-conductivity curve) is temperature independent [171] and any loss of it due to the elimination of quasiparticle excitations must be compensated by its gain elsewhere. In conventional superconductors the low-energy spectral weight lost due to the opening of the superconducting gap is transferred into the coherent dc response of the superconducting condensate at zero frequency and can be used to quantify the London penetration depth of a superconductor [172]. Such a redistribution of the overall conserved infrared spectral weight is called the Ferrell–Glover–Tinkham sum rule [68, 173]. In some exotic mechanisms of superconductivity, the spectral-weight redistribution has been suggested to involve not only infrared frequencies on the order of the superconducting energy gap but also energies much higher than those of the itinerant-charge-carrier response [174]. The suppression of the in-plane optical conductivity in the superconducting state due to the gapping of quasiparticles has been identified in all investigated iron-based superconductors with a variety of optical techniques, as illustrated in figure 14: single-crystalline Ba_1-xK_xFe₂As₂ [90, 99, 163, 175, 176], single-crystalline [112, 164, 177–179] and thin-film [165, 180–182] Ba(Fe_1-xCo_x)₂As₂, single-crystalline BaFe₂(As_1-xP_x)₂ [56], single-crystalline LiFeAs [114], single-crystalline [113, 183] and thin-film [166, 182] FeTe_1-xSe_x, as well as a static and pump-probe investigation of the infrared reflectance of a LaFeAsO_1-xF_x thin film [184]. All of these materials have been found to exhibit signatures of multiple superconducting gaps in their infrared optical conductivity, consistent with the inherently multiband character of the iron-based materials and in most cases only two different magnitudes of the superconducting gap have been identified despite the presence of five distinct sheets of the Fermi surface [10]. The infrared conductivity of the iron-based superconductors in the out-of-plane direction has only been investigated in two compounds, FeTe_1-xSe_x [185] and Ba(Fe_1-xCo_x)₂As₂ [186]. In a tour-de-force optical study, the latter work demonstrated that although it is notoriously difficult to obtain a fresh surface of good optical quality for infrared measurements in any iron-based material, such a surface, as opposed to its polished counterpart, is indispensable for the observation of the inherent out-of-plane optical response and the signatures of the superconducting state.

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In a single-band s-wave weakly coupled conventional superconductor, no infrared absorption is possible at energies smaller than the optical superconducting energy gap 2Δ due to the finite binding energy of the Cooper pairs making up the superconducting condensate [187, 188], which provides a simple experimental means for the determination of its value from the energy at which the optical conductivity first reduces to zero as a function of decreasing frequency (absorption edge). In many single-crystalline iron-based superconductors such an absorption edge has indeed been observed, as demonstrated in figures 14(a)–(d) and the corresponding optical superconducting energy gap 2Δ extracted. Its values for the optimally doped Ba_0.6K_0.4Fe₂As₂, $\text{BaF}{{\text{e}}_{1.87}}\text{C}{{\text{o}}_{0.13}}\text{A}{{\text{s}}_{2}}$, $\text{BaF}{{\text{e}}_{2}}{{\left(\text{A}{{\text{s}}_{0.67}}{{\text{P}}_{0.33}}\right)}_{2}}$, and $\text{FeT}{{\text{e}}_{0.55}}\text{S}{{\text{e}}_{0.45}}$ have been found to be approximately 19, 6.6, 10, and <3 meV (in the last case the absorption edge could not be reached) and agree very well with the values of the superconducting energy gap obtained using other experimental techniques [10, 167]. Yet in multiband superconductors, such as the iron-based materials, the situation is significantly complicated by the fact that several (up to five) bands contribute to the experimentally observed ac optical conductivity and the latter, strictly speaking, only reaches zero below the smallest optical superconducting energy gap and remains non-zero above it. This complication makes the accurate determination of the superconducting gaps more difficult and model-dependent, thus imparting additional significance to the development of a minimal effective low-energy model with clear justified microscopic underpinnings [99].

One of the most common ways to extract the values of superconducting energy gaps from optical-conductivity data is to use the weak-coupling Mattis–Bardeen expression for the optical conductivity of a single-band superconductor [187, 188] obtained in the framework of the Bardeen–Cooper–Schrieffer theory of superconductivity [189] or a linear combination thereof for multiband materials. The values of the superconducting energy gaps of various iron-based superconductors extracted using this approach can be found in the original works cited above and have also been listed and compared with those obtained using various experimental techniques in numerous superconducting compounds including conventional, heavy-fermion, and high-temperature copper-based superconductors in a comprehensive review presented in [167] and summarized in figure 15.

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In the case of the iron-based superconductors, however, the application of the Mattis–Bardeen expression or a combination thereof to describe the optical response in the superconducting state appears questionable. First of all, as already mentioned, this expression has been derived based on the weak-coupling microscopic theory of superconductivity developed by Bardeen, Cooper, and Schrieffer (BCS) and, therefore, is strictly speaking only applicable to the description of the optical response of weakly coupled superconductors. The coupling strength in the iron-based materials has, on the other hand, been shown to span a wide range from relatively weak to strong coupling, with a clear trend towards intermediate/strong coupling [167]. Secondly, the Mattis–Bardeen expression applies only to a single-band superconductor. It can, nevertheless, be readily generalized to the case of several bands, as has been demonstrated in [190]. However, this generalization is based on the same assumptions as the BCS theory itself, thus remaining in the weak-coupling regime also with respect to the coupling between different bands, while it is now widely accepted that in many iron-based materials the interband coupling between at least two of the bands is quite strong, as evidenced by the peak in the magnetic susceptibility at the wave vector connecting bands in the center and in the corner of the Brillouin zone, probed by inelastic neutron scattering [10], as well as an enhanced quasiparticle relaxation between analogous bands identified by means of time- and angle-resolved photoemission spectroscopy [191]. Finally, the Mattis–Bardeen expression is only applicable to the case of impurity scattering much larger than the corresponding coupling strength, i.e. in the limit of high impurity concentration. Some of the iron-based materials, like Ba(Fe_1-xCo_x)₂As₂, can indeed be expected to have relatively high levels of elastic impurity scattering, while others, like Ba_1-xK_xFe₂As₂ and BaFe₂(As_1-xP_x)₂, are considered to possess quite long quasiparticle mean free paths at least in some of the bands [41, 99, 192–194]. The above arguments show that while the application of the Mattis–Bardeen expression to some of the iron-based superconductors (namely, for weakly coupled compounds with weak interband scattering and a relatively high impurity concentration) could be partially justified, any adequate description of others requires a more complete theory of superconductivity which overcomes the above limitations [99].

The most sophisticated theory of superconductivity to date is the so-called Eliashberg theory of superconductivity, applicable at arbitrary coupling strengths both within and between all of the bands and at arbitrary impurity concentrations [195, 196]. Figure 16 shows a comparison of the experimental infrared conductivity of optimally doped Ba_1-xK_xFe₂As₂ and Ba(Fe_1-xCo_x)₂As₂ superimposed onto the prediction of an effective two-band Eliashberg theory of superconductivity obtained in a reduction from a microscopically more justified four-band theory constrained by the aforementioned clustering of the superconducting energy gaps into two groups by magnitude [99]. It can clearly be seen that the qualitative differences in the shape of the infrared conductivity between the two compounds are captured in the same theory, with only two parameters adjusted: the intraband impurity scattering rate and the plasma frequencies of the bands. The former change can be justified by the different location of the dopants, namely, in the superconducting iron planes in the case of Ba(Fe_1-xCo_x)₂As₂, which is expected to significantly disturb the coherent superconducting transport taking place in these planes, as compared to the substitution of the intercalating ion relatively far from the iron planes in Ba_1-xK_xFe₂As₂ [10]. The change of the plasma frequencies of the bands is to be expected due to the doping with charge carriers of opposite signs in these two cases. The above theory assumes that superconductivity in Ba_0.68K_0.32Fe₂As₂ is mediated by a boson with a characteristic energy of about 13 meV, consistent with the peak energy of the resonance mode in the magnetic susceptibility observed by means of inelastic neutron scattering [197] and thus with superconducting pairing mediated by antiferromagnetic spin fluctuations. The effect of various model parameters on the infrared conductivity predicted by the effective two-band Eliashberg theory used above can be analyzed in an interactive simulation in the supplementary material of [99].

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We can now apply the above reasoning to compare the shape of the optical conductivity across the entire family of the iron-based superconductors for which spectroscopic data in the superconducting state are available, shown in figure 14. It is immediately evident that the shape of the optical conductivity of optimally doped BaFe₂(As_1-xP_x)₂ (figure 14(c)) in the superconducting state compared to that in the normal state just above the superconducting transition temperature is very similar to the case of Ba_0.6K_0.4Fe₂As₂ shown in figure 14(a): down to a certain characteristic energy the superconductivity-induced suppression of the optical conductivity is small, while below that energy there is a gradual quasilinear fall-off in the low-temperature infrared conductivity until it reaches essentially zero, to the accuracy of the corresponding reflectance measurements. Based on this comparison one can conclude that optimally doped BaFe₂(As_1-xP_x)₂ must likewise be at least a moderately coupled superconductor with very low levels of elastic impurity scattering. The coupling strength can be estimated by the ratio of the value of the largest superconducting energy gap obtained, e. g., by means of angle-resolved photoemission spectroscopy $2\Delta \approx 8 \text{meV}$ [198] and the superconducting transition temperature of about 30 K at optimal doping: $2\Delta/{{k}_{\text{B}}}{{T}_{\text{c}}} \approx 6.5$—very close to that of optimally doped Ba_1-xK_xFe₂As₂ but with even lower superconducting transition temperature; see figure 15. Low levels of impurity scattering are eloquently confirmed by the observation of de Haas–van Alphen quantum oscillations, notoriously sensitive to disorder, starting from the terminal composition BaFe₂P₂ down to almost optimally doped BaFe₂(As_1-xP_x)₂ [41, 192, 194] as well as by the analysis of the collective vortex pinning in this material at optimal doping [193]. Additionally, and similarly to the comparison of Ba_1-xK_xFe₂As₂ and Ba(Fe_1-xCo_x)₂As₂ above, substitution in BaFe₂(As_1-xP_x)₂ occurs at the arsenic sites away from the iron planes in which the coherent superconducting transport takes place.

The shape of the optical conductivity of FeTe_1-xSe_x in the superconducting state compared to that in the normal state (figure 14(d)), on the other hand, is of the Mattis–Bardeen type and closely resembles that of optimally doped Ba(Fe_1-xCo_x)₂As₂. In view of the discussion above, this suggests that impurity scattering significantly perturbs coherent quasiparticle transport in the superconducting state. This conclusion is consistent with the very high doping levels required to achieve the maximal superconducting transition temperature, at which virtually every second tellurium atom is substituted by selenium. Sizable quasiparticle scattering is further confirmed by the clear observation of quasiparticle-interference patterns by means of scanning tunneling microscopy in this material [31].

In the case of LiFeAs, yet again, the shape of the optical conductivity is of the Mattis–Bardeen type (figure 14(e)). At first glance, this observation might lead one to conclude that, similarly to Ba(Fe_1-xCo_x)₂As₂ and FeTe_1-xSe_x, the impurity scattering rate is relatively high. However, even taking into account the well-known difficulty of controlling the lithium stoichiometry in LiFeAs [20, 199], recent scanning tunneling microscopy studies have shown that in the best samples the concentration of impurities can be very low [200]. Therefore, it is more likely that in the case of LiFeAs (assuming that the samples investigated by the authors of [114] were of comparable purity) the Mattis–Bardeen, rather than quasilinear, shape of the optical conductivity in the superconducting state results from the overall much weaker coupling suggested by the relatively small gap ratio $2\Delta/{{k}_{\text{B}}}{{T}_{\text{c}}}$ for the largest superconducting gap, located close to the BCS limit, as shown in figure 15.

Another set of instructive spectroscopic optical-conductivity data complementary to those discussed above has been obtained on thin films of two representative iron-based superconductors, Ba(Fe_1-xCo_x)₂As₂ and FeTe_1-xSe_x, as shown in figures 14(f) and (e), by means of terahertz transmission spectroscopy. This technique extends the spectral range covered by the traditional reflectance techniques and ellipsometry down to ∼5 cm⁻¹ and is sensitive to both the amplitude and phase of the transmitted signal, thus providing essential information about low-energy itinerant charge transport in the normal and superconducting state. The terahertz optical conductivity of both compounds shows several important common features. First of all, the superconductivity-induced suppression of the optical conductivity due to the opening of the superconducting energy gap is evident in both materials but, unlike in the case of single-crystalline compounds discussed above, the optical conductivity of thin-film samples has never been found to reach zero at any achievable terahertz frequency and always features some virtually frequency-independent contribution on the order of 1500–2500 Ω⁻¹ cm⁻¹ [165], [166], [180–182]. This residual conductivity has been argued to originate either in strong pair-breaking impurity scattering [181] or in the presence of nodes in the superconducting energy gap [165]. As pointed out by the authors of [165], the former mechanism appears inconsistent with the clear observation of a coherence peak in the optical conductivity of both compounds [165, 166, 180, 181], which is expected to be strongly suppressed by pair-breaking impurity scattering [201]. While the existence of nodes in the Ba(Fe_1-xCo_x)₂As₂ compound cannot be fully ruled out at present, it seems to be at odds with the experimental data obtained by means of angle-resolved photoemission spectroscopy [202] as well as some terahertz transmission measurements [180, 181]. In FeTe_1-xSe_x the existence of nodes is incompatible with the clear observation of a U-shaped rather than a V-shaped tunneling spectrum in the superconducting state by scanning tunneling spectroscopy [31], unambiguously proving the absence of quasiparticle excitations below the superconducting energy gap beyond thermal excitation [31]. This evidence indicates that neither the strong pair-breaking impurity scattering nor the existence of nodes provides a consistent explanation of the aforementioned residual conductivity and that it could, in fact, be extrinsic. For instance, such residual optical conductivity could come from absorption in an intermediate non-superconducting metallic layer between the substrate and the superconducting thin film. Indeed, strong evidence for the spontaneous formation of an intermediate several-nanometer-thick layer most likely composed of Fe atoms (along with possible inclusions in the bulk) in thin films grown using pulsed laser deposition has been reported for many different growth conditions [203–206]. Given that all of the above terahertz-transmission studies have been carried out on the thin films of iron-based superconductors grown by this method, the extrinsic character of the residual conductivity appears likely.

Notwithstanding the significant residual conductivity observed in transmission spectroscopy of the thin films of Ba(Fe_1-xCo_x)₂As₂ and FeTe_1-xSe_x, several features of superconductivity could be clearly identified in these measurements. The authors of [180] succeeded in directly observing one of the optical superconducting energy gaps 2Δ≈3.7 meV as the energy at which the real part of the terahertz conductivity drops to the background level. Furthermore, virtually all terahertz transmission studies have reported the presence of a coherence peak in the real part of the optical conductivity, which manifests itself as a slight enhancement of the optical conductivity at low enough energies just below the superconducting transition temperature as compared to its overall suppression at higher energies and lower temperatures. This behavior is a hallmark of superconductivity, very well understood in the conventional BCS and Eliashberg theories of superconductivity, and stems from the formation of highly coherent superconducting pairs [68] and/or the elimination of quasiparticle scattering channels below the optical superconducting energy gap [201]. It must be noted, however, that the existence of a coherence peak in the low-energy optical conductivity is a sufficient but not a necessary condition for superconductivity, as in certain circumstances it can be partially or fully suppressed [201, 207].

According to the Ferrell–Glover–Tinkham sum rule [68, 173], the missing area under the infrared conductivity curve as compared to that in the normal state is transferred into the coherent response of the superconducting condensate at zero frequency. It manifests itself in the most fundamental properties of superconductors: zero dc resistivity and the Meissner effect. The latter is characterized by the London penetration depth ${{\lambda}_{\text{L}}}$ for the magnetic field, which is related to the missing area SW via $\lambda _{\text{L}}^{-2}=8SW/{{c}^{2}}$ (in CGS units), where c is the speed of light. The missing area obtained from the integration of the optical conductivity of the iron-based superconductors typically gives a London penetration depth on the order of 2000–3500 Å, consistent with other measurements [10].

Intriguingly, the superconductivity-induced suppression of the optical conductivity with non-zero missing area has also been discovered in optimally doped Ba_0.68K_0.32Fe₂As₂ in the visible spectral range [90], at energies two orders of magnitude larger than the superconducting energy gap, as demonstrated in figures 17(a)–(c). This observation challenges the conventional theories of superconductivity, which only allow for the occurrence of the missing area at energies on the order of the superconducting energy gap [68, 187, 196]. Some exotic theories of superconductivity have proposed a mechanism by which the superconductivity-induced suppression of the optical spectral weight could extend to the spectral range of interband transitions [123, 124, 208]. The authors of [90] have demonstrated, however, that the observed effect can be understood phenomenologically in conventional terms by utilizing the inherently multiband nature of the iron-based superconductors. The suppression of an interband transition over its entire width with a local non-conservation of the spectral weight implies a change in the oscillator strength of this transition, which can take place due to the modification of the occupation in either initial or final states that its spans. Since all conventional superconductivity-induced modifications of the electronic structure and dynamics occur in the vicinity of the Fermi level within a few values of the superconducting energy gap, one may conclude that the only conventional way for an interband transition to feel the effect of superconductivity is for its initial or final states to be largely concentrated in this vicinity. However, this mechanism by itself would not entail any loss of spectral weight in the considered interband transition because the opening of the superconducting energy gap leads to the expulsion of electronic states from within the gap to above it with the total number of states conserved (illustrated in figure 17(d) with gray and blue lines and areas). Therefore, the corresponding modifications in the interband optical conductivity would be limited to small shifts/corrugations on the order of the superconducting energy gap [209] with the total spectral weight conserved. In the present case, on the other hand, it is then required that the number of states in the superconducting state be unequal to that in the normal state, as shown in figure 17(d) by the red line and area. In a conventional single-band superconductor such a scenario would be impossible and exotic mechanisms would have to be invoked to explain the observed suppression. The situation changes drastically in the case of multiband superconductivity. In the iron-based superconductors, due to the presence of multiple sheets of the Fermi surface, some of which are relatively strongly coupled to each other [10], a population redistribution could and indeed does occur dynamically between the strongly coupled sheets of the Fermi surface [191, 210] and could lead to a static population imbalance in the superconducting state should it be energetically favorable. This latter condition can be fulfilled in a multiband superconductor due to the well-known, albeit very small, effect of the change in the chemical potential upon entering the superconducting state [211, 212], proportional to the square of the superconducting energy gap. In case a material features different magnitudes of the superconducting energy gap on different sheets of the Fermi surface and/or a different character of the charge carriers (electrons versus holes), there will be a band- or orbital-specific shift of the chemical potential leading to a population redistribution between different bands. None of the existing theories of superconductivity takes this effect into account self-consistently. Albeit the missing area in the visible spectral range shown in figure 17(b) constitutes only a small fraction of that in the far-infrared (figure 17(a)), a simple estimate in the framework of the tight-binding nearest-neighbour approximation [123, 124] shows that it would entail a reduction of the electronic kinetic energy of 0.60 meV/unit cell in the superconducting state [90], should it contribute to superconducting pairing. This is close to the condensation energy ΔF (0) = 0.36 meV/unit cell obtained from specific-heat measurements on the same sample [213]. It thus remains to be seen whether the physics behind this phenomenon is of consequence for superconductivity of multiband materials.

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Arguably the most remarkable feature of the phase diagram of the iron-based superconductors is the proximity of the superconducting phase to antiferromagnetic order [10, 11]. With the exception of very few compounds (such as 1111-type materials and EuFe₂As₂), the superconducting transition temperature is maximized close to the zero-temperature end point of the antiferromagnetic/structural phase transition line underneath the superconducting dome, at which the long-range antiferromagnetic order continuously disappears and the corresponding antiferromagnetic spin fluctuations are expected to be strongest. This observation immediately suggested that superconductivity in the iron-based superconductors might be mediated by the quantum-critical fluctuations of the antiferromagnetic order parameter, similarly to the mechanism proposed for their high-temperature copper-based [78, 79, 125, 214] and heavy-fermion counterparts [215]. One of the expected manifestations of the quantum-critical regime is the non-Fermi-liquid linear temperature dependence of the dc resistivity in a funnel-shaped region of the phase diagram originating at the quantum critical point, as compared to the quadratic low-temperature behavior of the conventional Fermi liquid [78], due to quasiparticle scattering dominated by antiferromagnetic spin fluctuations (marginal Fermi liquid) [216]. Such behavior has indeed been identified in BaFe₂(As_1-xP_x)₂ [217, 218] along with a sharp peak in the zero-temperature London penetration depth near the doping level of the quantum critical point [81], which can be traced back to the enhancement of the quasiparticle effective mass, previously observed by means of de Haas–van Alphen measurements in the same material [41, 192, 194], by critical antiferromagnetic spin fluctuations [82].

Similar T-linear dc resistivity has been observed near optimal doping in Ba(Fe_1-xCo_x)₂As₂ and Ba(Fe_1-xRu_x)₂As₂ in [219, 220], respectively. Despite an overall very similar phase diagram of the hole-doped Ba_1-xK_xFe₂As₂ the temperature dependence of its dc resistivity at optimal doping was found to display a more complex behavior: quadratic at low temperatures with an inflection point and a trend towards saturation at higher temperatures [101, 221, 222], thus seemingly inconsistent with quasiparticle scattering dominated by critical antiferromagnetic spin fluctuations. However, similarly to the decomposition of the infrared conductivity of the 122 iron-based compounds into two distinct contributions [110] discussed in the previous section, it has been shown that this unusual temperature dependence of the dc resistivity can be described within the Eliashberg theory of normal metals by considering two electronic subsystems with very different elastic scattering rates and electron-boson interactions, one of which dominates the charge transport at low temperatures, while the other one—at high temperatures, giving rise to an inflection point in the temperature dependence [223]. A subsequent very detailed spectroscopic investigation of the temperature dependence of the infrared conductivity in Ba_0.6K_0.4Fe₂As₂ carried out in [176] uncovered, using an analogous two-component decomposition, that the quasiparticle scattering rate of the broad component is virtually temperature independent, while that of the narrow, coherent, contribution exhibits a linear temperature dependence, which, in turn, translates into the linear temperature dependence of the partial dc resistivity associated with this electronic subsystem. Thus it has been established that the temperature dependence of the dc resistivity of the coherent itinerant response in optimally doped Ba_0.6K_0.4Fe₂As₂ is, in fact, consistent with quasiparticle scattering dominated by marginal-Fermi-liquid spin fluctuations but is masked by multiband effects in raw transport data. Eliminating the dc value of the temperature-independent incoherent term obtained from the two-component analysis of the infrared-conductivity spectra one may extract the doping dependence of the quantum-critical T-linear and the conventional Fermi-liquid T² contributions to the dc resistivity based on comprehensive transport data. This analysis has been carried out in [218] on a representative set of electron-doped Ba(Fe_1-xCo_x)₂As₂, isovalently substituted BaFe₂(As_1-xP_x)₂, and hole-doped Ba_1-xK_xFe₂As₂ based on the same parent compound, BaFe₂As₂, and is juxtaposed with the phase diagrams of these materials in figure 18. A recent magneto-transport investigation of the parent EuFe₂As₂ compound under high pressure [224] has revealed the presence of a similar T-linear dependence of the in-plane dc resistivity and the recovery of the conventional quadratic temperature dependence upon application of an external magnetic field, which strongly suggests that the linear temperature dependence in the nearly optimally doped superconducting compounds does indeed originate in strong coupling to spin fluctuations.

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While the occurrence of the linear temperature dependence of the in-plane dc resistivity near optimal doping has been reliably established in the majority of iron-based superconductors and thus strongly suggests the universal relevance of underlying quasiparticle interaction for the mechanism of superconductivity, the possible existence and importance of the antiferromagnetic quantum critical point underneath the superconducting dome near optimal doping is under debate. As discussed above, in the case of BaFe₂(As_1-xP_x)₂ significant experimental evidence has been furnished by means of various experimental techniques in favor of the existence of the quantum critical point, manifested in the enhancement of the quasiparticle effective mass upon approaching the optimal doping, as well as of a funnel-shaped region of the phase diagram with the linear temperature dependence of the dc resistivity. Similarly, magnetoelastic studies of Ba(Fe_1-xCo_x)₂As₂ across its phase diagram have revealed the divergence of the nematic susceptibility near the optimal doping and thus strongly suggest the existence of a nematic quantum critical point at optimal doping [84]. Nuclear-magnetic-resonance investigations on the same material further corroborate the existence of a quantum critical point [150, 225]. On the other hand, the aforementioned investigation of the magnetotransport in the parent EuFe₂As₂ compound under pressure reported the absence of any detectable enhancement of the quasiparticle effective mass across the optimal doping level [224]. Finally, the phase diagram of the 1111-type iron-based materials shows a rich variety of qualitatively different phase diagrams. The LaFeAsO_1-xF_x and NdFeAsO_1-xF_x materials feature a sharp disappearance of antiferromagnetism at the border with the superconducting phase in a first-order phase transition [226, 227]. The phase diagram of CeFeAsO_1-xF_x was found to exhibit the complete continuous disappearance of antiferromagnetism with doping before the onset of superconductivity [14], while that of the Sm-based compound—to possess a large region of coexistence of superconductivity and antiferromagnetism, with strong spin fluctuations extending to the very overdoped region [228], thus providing evidence for both the existence of a quantum critical point underneath the superconducting dome (see also [229]) and the importance of spin fluctuations for superconductivity. A recent nuclear-magnetic-resonance investigation of the phase diagram of isovalently substituted $\text{LaFeA}{{\text{s}}_{1-x}}{{\text{P}}_{x}}\text{O}$ provided another example of an 1111-type material in which quantum criticality seems to bear upon superconductivity [230]. These contrasting data across different classes of iron-based superconductors indicate that quantum criticality in these compounds is material-dependent and in some of them might not bear directly on the occurrence of superconductivity.

A recent systematic analysis of the optical conductivity spectra of several representative 122-type iron-based compounds across their respective phase diagrams in the framework of the two-component free-charge-carrier response, shown in figure 19, has revealed several interesting trends [218]. First of all, it has discovered the presence of a relatively weak dependence of the broad incoherent contribution on doping. Secondly, and more importantly, it found that superconductivity in these materials only occurs when the spectral weight of the narrow Drude contribution to the optical response is relatively small (the so-called 'bad-metal' behavior) and fades away as the latter becomes much larger and the material—more metallic. Based on the comparison of their results with the existing experimental data the authors conclude that the decrease of the spectral weight of the narrow component in the superconducting compounds most likely originates in the corresponding enhancement of the quasiparticle mass renormalization and thus strengthening of electronic correlations.

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Strong coupling to spin fluctuations strongly suggested by the observation of the T-linear temperature dependence of the in-plane dc resistivity discussed above implies a sizable amount of inelastic scattering at the characteristic energies of these excitations in the normal state. It is tempting to associate the optical-conductivity contribution resulting from such scattering with the broad incoherent electronic background observed in all investigated iron-based superconductors, particularly in view of the unphysically small values of the quasiparticle mean free path obtained under the assumption of this electronic background entirely originating in elastic scattering, as discussed in the previous section. On the other hand, the broad component's origin in the inelastic scattering due to spin fluctuations seems to be at odds with the rather weak temperature and doping dependence of its scattering rate [111, 176, 218, 231], compared to the corresponding temperature dependence of the optical conductivity predicted in the framework of the marginal-Fermi-liquid theory [201]. This issue requires further systematic experimental investigation.