Table of contents

The discovery of new natural and artificial materials has revolutionized condensed matter physics and our views on the role of correlations between electrons. Novel properties such as high-temperature superconductivity and colossal magnetoresistance discovered in these materials have overturned our conventional representations of condensed matter physics and pushed us to reconsider many well-established concepts. For example, we must treat the Coulomb interaction between electrons far beyond perturbation theory; we must recall long-forgotten ideas of electronic phase separation introduced originally by Nagaev in the 1960s; we must reconsider the role of electron--phonon and electron--magnon interactions, orbital degrees of freedom, the Rashba effect and many other aspects of condensed matter physics that are becoming increasingly important.

In many novel materials, such as the two-dimensional electron gas, the energy associated with the Coulomb interaction is typically of the order of (or even larger than) the kinetic energy of electrons or the Fermi energy. Therefore perturbation theory and associated renormalization group methods are not applicable to these situations and we may expect to find a novel state of matter associated with correlation effects. It is worth mentioning the known examples of these states proposed recently, such as marginal Fermi liquids, novel metal--insulator phase transitions in the two-dimensional electron gas associated with new metallic and insulating states, structured liquids, microscopic electronic phase separations, stripes, strings, polarons and others. The discussion of these states is now on the frontier of modern condensed matter physics and is partially covered in this special issue.

The demand to treat the Coulomb interaction properly has stimulated a development of many-body theory, which considers correlations as fully as possible. Strong correlations may play an important role in the dynamics of the electronic system. In a two-dimensional electron gas subjected to a transverse magnetic field, correlations associated with the Coulomb interaction transform normal electrons into composite fermions consisting of electrons with integer magnetic fluxes attached to them. The quasiparticle excitations, such as holes, arising in these systems may have fractional statistics (the so-called anyons).

Thus, a strong Coulomb interaction in novel materials may change the face of electrons, transforming their statistical properties. Such a phenomenon has already been established in quasi-one-dimensional materials, where an arbitrarily weak interaction transforms the Fermi liquid state associated with fermions into a bosonic Luttinger liquid. Will this effect happen in other types of novel materials? Future studies will answer this question. Many-body correlations may change the nature of the Coulomb interaction between electrons, leading to screening and over-screening effects. In the latter case the Coulomb repulsion between electrons will be transformed into a mutual attraction at certain distances. At some critical electron density, when the average distance between electrons is within this attractive region, this over-screening effect will obviously lead to the formation of electronic clusters and eventually to the formation of a clustered liquid or stripes. A similar effect may also arise through lattice distortions or electron--phonon interaction.

In many new materials there exists an insulating antiferromagnetic state, which is transformed under doping, eventually leading to a metallic state. The evolution of the antiferromagnetic state under doping has been a central issue in scientific discussions for decades. How the metal--insulator transition arises and the nature of the eventual metallic state are still not clear, although many interesting ideas are competing. The motion of a single doped hole leaves a trace behind, a piece of a single domain wall. Such pieces of domain walls arising from the motion of holes may be self-organized into a network of channels or a network of string and stripes. Such a network serves as a roadmap for hole motion and may be responsible for anomalies in physical properties of novel materials.

The Department of Physics at Loughborough University held an international workshop on Strongly Correlated Electrons in New Materials (SCENM02) which took place in conjunction with the annual meeting of the Condensed Matter Theory Group of the Institute of Physics on 14--17 December 2002. There were about 40 invited speakers and many poster presenters from a total of 12 countries, covering many aspects of the physics of colossal magnetoresistance manganites, high-temperature superconductors, two-dimensional electron gases displaying metal--insulator transition, electron--hole liquids, hydrogen at high pressures, semiconductor superlattices, magnetic multilayers and other novel materials. The abstract book is available on the physics department website at http://www.lboro.ac.uk/departments/ph/events/Abstracts.pdf. In this special issue we have collected papers covering these and many other important aspects of correlated electrons in new materials presented at the international workshop. We hope that this issue will stimulate further development in the physics of correlated electrons and lead to many new phenomena still waiting to be discovered.

In this paper, the history of the discovery of the linear magnetoresistance in metals by Kapitza from 1928–1929 and its explanation are described. Actually, Kapitza discovered two different phenomena. One of them, the linear magnetoresistance at classically large magnetic fields in polycrystalline samples of metals, having open Fermi surfaces, was explained by Lifshits and Peschansky in 1958. The other phenomenon is the quantum linear magnetoresistance appearing in metals, or semimetals, with a small concentration of carriers and a small effective mass, when only the lowest Landau band participates in the conductivity. Manifestations of this unusual phenomenon in different materials are described.

We show the key role of the elastic local strain (or micro-strain) ε of the CuO₂ lattice in the phase diagram of cuprate superconductors. The superconducting critical temperature T_c(δ, ε) is shown to be a function of two variables, the doping δ and the microstrain ε.

The coupled cluster method (CCM) of microscopic quantum many-body theory has become an ab initio method of first choice in quantum chemistry and many fields of nuclear, subnuclear and condensed matter physics, when results of high accuracy are required. In recent years it has begun to be applied with equal success to strongly correlated systems of electrons or quantum spins defined on a regular spatial lattice. One regularly finds that the CCM is able to describe accurately the various zero-temperature phases and the quantum phase transitions between them, even when frustration is present and other methods such as quantum Monte Carlo often fail. We illustrate the use and powerfulness of the method here by applying it to a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest neighbour bonds. The model exhibits the physically interesting phenomenon of competition between magnetic order and dimerization. Results obtained for the model with the CCM are compared with those found from spin-wave theory and from extrapolating the results of exact diagonalizations of small lattices. We show that the CCM is essentially unique among available methods in being able both to describe accurately all phases of this complex model and to provide accurate predictions of the various phase boundaries and the order of the corresponding transitions.

We study the possibility of nanoscale phase separation in manganites in the framework of the double-exchange model. The homogeneous canted state of this model is proved to be unstable towards the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyse the quantum effects related to the tails of electronic wave function and a possibility of electron hopping in the antiferromagnetic background. We find that these effects lead to the formation of the threshold for the polaronic state.

We review recent work on frustrated electronic phase separation in strongly correlated systems and the connection between electronic phase separation at a mesoscopic scale and structural phase separation at larger scales associated with volume instabilities. The former is due to the competition between phase separation tendencies and the long-range Coulomb interaction and surface energy effects. Above a critical value of the Coulomb interaction electronic phase separation is not possible and a volume instability arises. The system shows the tendency to phase separate into two neutral phases with different unit cell volumes.

We introduce an elementary model based upon the orientational nature of orbitals, which may arise from the influence of a cubic-symmetric crystal field. We focus on orbital ordering induced by correlated charge motion: a phenomenon often ignored. Motivated by the Nagaoka ferromagnetism, we seek the analogue single-hole result for our model in the strong-coupling regime. For two-fold degenerate orbitals on the square lattice, we show that the system promotes stripe phases as energetically favourable. In such phases, the system breaks the symmetry, with lines of one species of fermion being periodically separated and the other species filling in the gaps. For the simplest form of stripe, all periodicities are exactly degenerate, but we can show rigorously that such states are actually higher in energy than a small number of more exotic states which show the same long-range behaviour but are locally disrupted from the simplest case. Such states have a preferred periodicity of three.

Orbital ordering occurs in many transition metal compounds with Jahn–Teller ions (Cu²⁺, Mn³⁺, low-spin Ni³⁺, Ti³⁺ etc). It plays an important role in these materials. At the same time, exchange interactions in orbitally degenerate systems are inherently frustrated, even in materials with simple crystal lattices. We discuss the origin of this frustration, considering in detail materials with cubic and triangular lattices of transition metal ions. We also discuss possible types of ground states of such systems, e.g., disordered orbital liquids and ordering due to the order-from-disorder mechanism.

A large body of experimental evidence suggests that the decay of the false vacuum, accompanied by quantum pair creation of soliton domain walls, can occur in a variety of condensed matter systems. Examples include nucleation of charge soliton pairs in density waves (e.g., Miller J H Jr et al 2000 Phys. Rev. Lett. 84 1555) and flux soliton pairs in long Josephson junctions. Recently, Dias and Lemos (2001 J. Math. Phys. 42 3292) have argued that the mass m of the soliton should be interpreted as a line density and a surface density, respectively, for (2 + 1)-D and (3 + 1)-D systems in the expression for the pair production rate. As the transverse dimensions are increased and the total mass (energy) becomes large, thermal activation becomes suppressed, so quantum processes can dominate even at relatively high temperatures. This paper will discuss both experimental evidence and theoretical arguments for the existence of high-temperature collective quantum phenomena.

We examine a mixture of electrons and holes in semiconductors. It is well known that in such a system the effective Coulomb interaction is perfectly screened at long distances, which leads to Mott's metal–insulator phase transition. We show that the screening is not monotonic and at intermediate ranges there are regions of over-screening, which at low densities become strong enough to destroy the homogeneous mixture by clustering charges. We suggest that this phenomenon is responsible for the broad density distribution of the electron–hole liquid and the condensed plasma phase in silicon suggested by Smith and Wolfe (1995 Phys. Rev. B 51 7521). When the hole mass is set equal to the proton mass we can study properties of the metallic hydrogen and show that at high pressures there is a phase transition into a crystal phase of protons.

We have measured the effective mass, m, and Landé g factor in very dilute two-dimensional electron systems in silicon. Two independent methods have been used: (i) measurements of the magnetic field required to fully polarize the electrons' spins and (ii) analysis of the Shubnikov–de Haas oscillations. We have observed a sharp increase of the effective mass with decreasing electron density while the g factor remains nearly constant and close to its value in bulk silicon. The corresponding strong rise of the spin susceptibility χ ∝ gm may be a precursor of a spontaneous spin polarization; unlike in the Stoner scenario, it originates from the enhancement of the effective mass rather than from the increase of g factor. Furthermore, using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization and, therefore, its increase is not related to spin exchange effects, in contradiction with existing theories. Our results show that the dilute 2D electron system in silicon behaves well beyond a weakly interacting Fermi liquid.

In different 2D semiconductor systems we study the interaction correction to the Drude conductivity in the intermediate and ballistic regimes, where the parameter k_BTτ/ℏ changes from 0.1 to 10 (τ is momentum relaxation time). The temperature dependence of the resistance and magnetoresistance in parallel and perpendicular magnetic fields is analysed in terms of the recent theories of electron–electron interactions in systems with different degree of disorder and different character of the fluctuation potential. Generally, good agreement is found between the experiments and the theories.

Domain walls can significantly modify electronic properties of ferromagnetic metals. In this paper we consider theoretically the influence of domain walls on transport properties of ferromagnetic materials and the results are compared with recent experiments. In the case of diffusive transport through a thick domain wall, the semiclassical approximation is applied and a local spin transformation is performed, which replaces the system with a domain wall by the corresponding system without a domain wall but with an additional gauge field. Due to a redistribution of single-particle electron states at the wall, one obtains then either negative or positive contributions to resistivity. The situation is different for very narrow and/or constrained domain walls. In such a case, the semiclassical approximation is not valid. Instead of this the approach based on scattering matrix is applied. The domain wall then gives rise to a large positive contribution to electrical resistivity. The corresponding magnetoresistance can be therefore very large, which is in agreement with recent experiments. The limiting case of narrow domain walls in systems with a single conduction channel is analysed in detail, with the effects due to electron–electron interaction taken into account. In this particular case the magnetoresistance due to a domain wall can be extremely large.

We present a many-body approach to the electronic and magnetic properties of the (multiband) Kondo-lattice model with ferromagnetic interband exchange. The coupling between itinerant conduction electrons and localized magnetic moments leads, on the one hand, to a distinct temperature dependence of the electronic quasiparticle spectrum and, on the other hand, to magnetic properties such as, e.g., the Curie temperature T_C or the magnon dispersion, which are strongly influenced by the band electron self-energy and therewith in particular by the carrier density. We present results for the single-band Kondo-lattice model in terms of quasiparticle densities of states and quasiparticle band structures and demonstrate the density dependence of the self-consistently derived Curie temperature. The transition from weak-coupling (RKKY) to strong-coupling (double exchange) behaviour is worked out. The multiband model is combined with a tight-binding-LMTO band structure calculation to describe real magnetic materials. As an example we present results for the archetypal ferromagnetic local-moment systems EuO and EuS. The proposed method avoids the double counting of relevant interactions and takes into account the correct symmetry of atomic orbitals.

We derive gap equations for superconductivity in coexistence with ferromagnetism. We treat singlet and triplet states with either equal spin pairing (ESP) or opposite spin pairing (OSP) states, and study the behaviour of these states as a function of exchange splitting. For the s-wave singlet state we find that our gap equations correctly reproduce the Clogston–Chandrasekhar limiting behaviour and the phase diagram of the Baltensperger–Sarma equation (excluding the FFLO region). The singlet superconducting order parameter is shown to be independent of exchange splitting at zero temperature, as is assumed in the derivation of the Clogston–Chandrasekhar limit. P-wave triplet states of the OSP type behave similarly to the singlet state as a function of exchange splitting. On the other hand, ESP triplet states show a very different behaviour. In particular, there is no Clogston–Chandrasekhar limiting and the superconducting critical temperature, T_C, is actually increased by exchange splitting.

We consider a possible mechanism of the charge stripes in the high-T_c cuprates, based on some additional interactions in the two-dimensional t–J model; the next-nearest-neighbour and/or four-spin (ring) exchange interactions. The many-hole correlation functions obtained by numerical exact diagonalization of a finite-cluster t–J model including the correction terms indicate the realization of the mechanism and give some preliminary phase diagrams. A realistic combination of these additional terms is also studied.

We have applied the method of point-contact (PC) spectroscopy to conductors with a charge-density-wave (CDW) ground state. Recent experimental results of the investigation of characteristics of PC formed between a normal metal (N) and different CDW conductors are reported. For a uniform N–CDW boundary, we show that the interaction of carriers injected from the normal metal with the CDW results in their reflection without changes in the sign of the charge but with a momentum transfer 2p_F to the condensate of electron–hole pairs carried away from the N–CDW interface. In the case of a non-uniform N–CDW boundary (direct point contact), a strong local CDW deformation, due to a band bending effect, was observed in materials with a semiconducting ground state. The chemical potential can be strongly modified, changing the conductivity type in the vicinity of the PC. It was shown that, in the case of a CDW conductor with a metal or semimetal ground state, the band bending effect is negligible (because of the screening of the electric field by remaining normal carriers) and the spectroscopy of the Peierls energy gap is possible.

Using small staked junctions of high quality we have measured interlayer tunnelling spectra of the layered quasi-one-dimensional material NbSe₃. We identified a number of new features in the spectra: zero bias conductance peak (ZBCP), charge density wave (CDW) gap structure for lower and upper CDW, the sub-gap structure inside the CDW gap. The ZBCP dominates in low-temperature spectra. We discuss its origin as being related to the interlayer coherent tunnelling of the carriers uncondensed into CDW. We found that ZBCP is sensitive to magnetic field and its orientation. The field perpendicular to the layers broadens ZBCP while the parallel field narrows it. We consider the sub-gap structure as associated with self-localized states inside the gap.

Superconducting and striped states under lattice distortions are investigated for high-T_c cuprates based on the quantum variational Monte Carlo method as the ground state of the two-dimensional (three-band) Hubbard model. We study the wavefunctions for the correlated condensed states: superconductivity, antiferromagnetism, inhomogeneity and their coexistent state with on-site Gutzwiller correlation. The model parameters are chosen for cuprate high-T_c superconductors such as La_1−xSr_xCuO₄ with x < 0.125. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and superconductivity (SC) in the low-temperature tetragonal (LTT) phase. We show that the total energy of the inhomogeneous d-wave SC state with vertical stripes having half-filled holes is lower than that of competing spin-density wave (SDW) states. The SC order parameter oscillates according to inhomogeneity in the antiferromagnetic background, and the SC condensation energy is reduced as the doping rate decreases in the underdoped region. The decreasing tendency of the SC condensation energy with decreasing doping is in accord with that of the specific heat data. In the low-temperature orthogonal (LTO) phase the diagonal stripes are stabilized in the lightly doped region for less than 5% doping. We also examine the stability of the mixed phase of LTT–HTT coexisting with stripes.

We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one-dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intra-pair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1d and 2d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole motion in the CuO₂ planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone.

We study a three-band effective model of a CuO₂ plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO₂ lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory.

We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO₂ plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0.

Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid.

These predictions are in contrast to those of the t–J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.

We have succeeded in quantizing massive collective gauge fields around the doped hole by using the theoretical formula, which is based on the gauge-invariant effective Lagrangian density, in underdoped cuprates. Quantized massive gauge fields, which are induced around the doped hole, explain naturally the broad spectra of angle-resolved photoemission around the hot spot, short-range spin fluctuations and anomalous transport properties in underdoped cuprates.

We revisit the old problem of exotic superconductivity as Cooper pairing with finite angular momentum emerging from a central potential. Based on some general considerations, we suggest that the phenomenon is associated with interactions that keep electrons at some particular, finite distance r₀, and occurs at a range of intermediate densities n ∼ 1/r³₀. We discuss the ground state and the critical temperature in the framework of a standard functional-integral theory of the BCS to Bose crossover. We find that, due to the lower energy of two-body bound states with l = 0, the rotational symmetry of the ground state is always restored on approaching the Bose limit. Moreover in that limit the critical temperature is always higher for pairs with l = 0. The breaking of the rotational symmetry of the continuum by the superfluid state thus seems to be a property of weakly-attractive, non-monotonic interaction potentials, at intermediate densities.

We investigated dynamical effects in a system of magnetic multilayers which arise at different rates of change of the external field. Our studies have been stimulated by recent experiments indicating nontrivial magnetic dynamics in these systems.

To describe a system consisting of magnetic layers, we have used conventional Bloch equations. A time-dependent external magnetic field has been applied, but no dissipation effects have been taken into account. We have studied the time development and instabilities of the regular behaviour of this system numerically. We found local energy excitations (breathers) and chaotic transients. The behaviour and the final configurations can strongly depend on the initial conditions, and the strength of the external field at an earlier time. We observed some sudden switching between two remarkably different states. The series of bifurcations has been found.

The insulating Mott state is formed due to repulsive electron–electron Coulomb interaction in the presence of the lattice (or in other words, due to electron–electron Umklapp processes). The second moment conductivity sum rule is derived, and it allows us to evaluate the strength of Umklapp scattering and the static electron–lattice energy. Mid-infrared spectra of current–current and density–density correlation functions in cuprates are suggested as evidence of strong Umklapp scattering.

An analytical approach has been developed for the electron–phonon coupling in the Holstein–Hubbard model. The Hubbard U is treated approximately by the slave-boson approach. We show that our approach is flexible and physically clear because it is based on perturbation theory. When the dimensionless ratio ω_p/2Dt is small, ω_p/2Dt ≪ 1, our result is similar to that of the Migdal–Eliashberg theory. When ω_p/2Dt > 1, our result approaches that of the Lang–Firsov transformation and small polaron theory. We have calculated the effective mass of electrons at the Fermi surface to show that the new perturbation approach works well in the intermediate region where ω_p/2Dt ∼ 1.