Table of contents

The 5th International Conference on the Intrinsic Josephson Effect and Plasma Oscillations in High-T_c Superconductors (known as `PLASMA' for short) took place in London from July 17th to 19th 2006. The meeting was organised jointly by the Superconductivity Group of the Institute of Physics and the European Science Foundation network `Arrays of Quantum Dots and Josephson Junctions' (AQDJJ). It was sponsored by the UK Engineering and Physical Sciences Research Council, AQDJJ, the Japan Society for the Promotion of Physics and the National Institute of Materials Science (NIMS). The meeting was chaired by Paul Warburton of University College London who wishes to put on record his thanks to the conference sponsors for their generosity, without which the conference could not have taken place.

Since the previous PLASMA conference in Tsukuba in 2004 the most significant advance in intrinsic Josephson junction (IJJ) research has arguably been the observation of macroscopic quantum tunnelling in IJJs. At the time of the conference this had been observed by both the RIEC/NIMS/AIST collaboration in Japan and by Paul Müller's group in Erlangen. We therefore felt that the conference presented an ideal and timely opportunity for the IJJ community to learn from the more established community of researchers on macroscopic quantum phenomena in low-T_c superconductors---and indeed vice versa. As a result a number of leading researchers from the field of low-T_c Josephson qubit devices gave several illuminating presentations. Other sessions included those on Josephson vortex dynamics in layered systems and terahertz oscillations in IJJs, in addition to a lively poster session on the first evening. The conference was rounded off by an excellent summary of the highlights of the meeting given by Professor Hu-Jong Lee.

The conference organisers would like to thank all those who made the meeting possible and contributed to its smooth running. In addition to the international organising committee, local organising committee, sponsoring organisations and session chairs (who we hope will forgive us if we use lack of space as justification for not naming them individually), special thanks are due to Jasmina Bolfek-Radovani of the Institute of Physics for her day-to-day running of the conference which was of the highest standard possible.

The Josephson fluxon behaviour in layered BSCCO-type single crystals is modelled by coupled long Josephson junctions described by coupled sine–Gordon equations. Among all the possible solutions, particularly interesting are the so-called in-phase fluxon solutions with coherent motion of all the fluxons. Recently, generation of electromagnetic waves at almost terahertz (THz) frequencies in BSCCO single crystals was reported. In order to maximize the power of such generation, these in-phase fluxon solutions are essential. Two different avenues to obtain in-phase fluxon motion have been suggested, i.e. either using the interaction with a cavity to phase lock the fluxon motion or applying a large magnetic field to create in-phase flux flow solutions. We have numerically considered both mechanisms. The results provide an understanding of the system and a guidance to experimentalists looking for THz generation in BSCCO.

We have investigated macroscopic quantum tunnelling (MQT) in in-plane high-T_c superconductor Josephson junctions and the influence of the nodal-quasiparticle and zero energy bound states (ZES) on MQT. We have shown that the presence of ZES at the interface between the insulator and the superconductor leads to strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably suppressed in comparison with c-axis junctions in which ZES are completely absent.

The quantum dynamics of Bi₂Sr₂CaCu₂O_8+δ intrinsic Josephson junctions (IJJs) is studied based on escape rate measurements. The saturations observed in the escape temperature and in the width of the switching current below 0.5 K (= T^*) indicate the transition of the switching mechanism from thermal activation to macroscopic quantum tunnelling. It is shown that the switching properties are consistently explained in terms of the underdamped Josephson junction with a quality factor of 70 ± 20 in spite of possible damping due to the nodal quasiparticles of d-wave superconductivity. The present result gives the upper limit of the damping of IJJs.

We have measured overlapping linear and non-linear branches in the hysteretic current–voltage characteristics of an intrinsic Josephson junction array fabricated from a Tl₂Ba₂CaCu₂O₈ thin film. Analysis of the retrapping voltages and critical currents of the junctions confirms that the linear branches correspond to moderately-damped SIS junctions while the non-linear branches correspond to more lightly-damped SIS junctions.

We have made a numerical study of the effect of thermal fluctuations on Josephson vortex dynamics in a stack of intrinsic Josephson junctions. Our simulations successfully reproduced the experimental results such as the field dependence of the critical current, the noise-rounded current–voltage characteristics and a periodic oscillation of the Josephson vortex flow resistance. It was confirmed that the oscillation period of the Josephson vortex flow resistance is related to the modulation of the critical current rather than the vortex lattice structure. We found that in the dynamic state the triangular vortex lattice becomes stable independent of the field even at zero temperature. Furthermore, at finite temperature, a thermally activated disordered vortex flow is observed in a low-bias region where the Lorentz force is not large enough to induce the collective flow of vortices.

In order to construct a theory for photon-assisted macroscopic quantum tunnelling (MQT) in intrinsic Josephson junctions, we revisit the model of capacitively coupled intrinsic Josephson junctions and clarify how the quantized energy levels in the N-junction stacked system distribute inside a valley of the Josephson sinusoidal potential. Furthermore, we reveal that the MQT escape rate from the single-plasmon states to the uniform voltage ones by microwave irradiation is proportional to the square of the junction number (N²) in multi-photon processes. This result is consistent with the recent finding in Bi-2212 intrinsic Josephson junctions by Jin et al 2006 Phys. Rev. Lett. 96 177003.

Ultra-thin pieces of Bi₂Sr₂CaCu₂O_8+δ single crystals (d<100 nm) can be isolated by cleaving pre-etched mesas off the main crystal using a flip-chip technique. Further thinning of the pieces by Ar-ion milling down to a few nanometres reveals the superconductor–insulator transition in the samples. In a refined technique, a precise control of the etching depth from both sides of the crystal makes it possible to form stacks of intrinsic Josephson junctions (IJJs) inside these ultra-thin single crystals. The stacks can be tailor-made to any small height (0–9 nm) thus assuring any low number of IJJs in the stacks (N = 0–6). Several features can be seen in the current–voltage (I–V) characteristics of these stacks, and therefore dI/dV (V) curves contain several peaks that behave differently with N. While the high-bias peaks shift in the normalized voltage V/N, the low-lying peaks at V/N≈32.4 ± 0.8 mV are N-independent. These peaks are reproducibly found in stacks of various lateral dimensions (0.5–11 µm², N = 1...5) in a wide temperature range (T<0.8T_c). We briefly discuss possible reasons for the small values of the peak voltage.

The influence of optical phonons on the stability of the in-phase regime of Josephson vortices motion is studied on the basis of the expression of dielectric permittivity derived using a simple hydrodynamical description of a layered superconductor. Contributions from superconducting condensates, normal quasiparticles and from optical phonons taking into account spatial dispersion are considered self-consistently. The dispersion characteristics of linear waves are analysed. It is shown that the spontaneous establishment of the in-phase regime of vortices motion is possible near optical phonon frequencies in layered superconductors.

We study branching in the current–voltage characteristics of the intrinsic Josephson junctions of high-temperature superconductors in the framework of the capacitively coupled Josephson junction model with diffusion current. A system of dynamical equations for the gauge-invariant phase differences between superconducting layers for a stack of ten intrinsic junctions has been numerically solved. We have obtained a total branch structure in the current–voltage characteristics. We demonstrate the existence of a 'breakpoint region' on the current–voltage characteristics and explain it as a result of resonance between Josephson and plasma oscillations. The effect of the boundary conditions is investigated. The existence of two outermost branches and correspondingly two breakpoint regions for the periodic boundary conditions is shown. One branch, which is observed only at periodic boundary conditions, corresponds to the propagating of the plasma mode. The second one corresponds to the situation when the charge oscillations on the superconducting layers are absent, excluding the breakpoint. A time dependence of the charge oscillations at breakpoints is presented.

We have found previously periodic oscillations in Josephson-vortex (JV) flow resistance against parallel magnetic fields with a c-axis current applied to the rectangle-shaped intrinsic Josephson junctions (IJJs) of Bi₂Sr₂CaCu₂O_8+y. We have tried to study the JV flow resistance in annular-type IJJs, and have found oscillations with several periods determined by the effective width direction perpendicular to the field and the current, which proves there to be a three-dimensionally ordered state of JVs even in non-continuous media. For annular-type junctions, we propose the possibility of estimating the correlation length of JVs for forming a JV lattice.

We use the temperature dependent c axis critical current and characteristic gap voltage as temperature gauges to assess the self-heating in stacks of intrinsic Josephson junctions etched out from the ultrathin Bi₂Sr₂CaCu₂O_8+δ (BSCCO) single crystals. The thermal resistance which characterizes the overall cooling efficiency is found to be ∼120–160 K mW⁻¹ for the two stacks studied. This value is in agreement with earlier reports for stacks of similar geometry, while it is about two to three times higher than for simple mesas made on the surfaces of mm-size BSCCO single crystals. The suggested method can guarantee the validity of the temperature estimations inside the stacks of various geometries and different cooling efficiencies without the need for attaching additional thermometers.

We consider the problem of c-axis transport in double-layered cuprates, in particular with reference to Bi₂Sr₂CaCu₂O_8+δ compounds. We exploit the effect of the two barriers on the thermal and tunnel transport. The resulting model is able to describe accurately the normal state c-axis resistivity in Bi₂Sr₂CaCu₂O_8+δ, from the underdoped side up to the strongly overdoped. We extend the model, without introducing additional parameters, in order to allow for the decrease of the barrier when an external voltage bias is applied. The extended model is found to describe properly the c-axis resistivity for small voltage bias above the pseudogap temperature T^*, the c-axis resistivity for large voltage bias even below T_c, and the differential dI/dV curves taken in mesa structures.

We describe new phenomena arising in long and extended Josephson junctions associated with the two-dimensional character of these junctions. A vortex in such junctions has additional degrees of freedom related to its length. We investigate the behaviour of a Josephson vortex in curved waveguides. As a result we have proposed how to increase transmission properties of a curved waveguide. Moreover, there may arise a flux cloning phenomenon. In this phenomenon the vortex may split into two or more new vortices at the special T, Y or any multiple shaped junction. We describe a series of new devices, the operation of which is based on flux cloning.

We present a study of the switching current distribution from the zero-voltage state to a nonzero-voltage state in Bi₂Sr₂CaCu₂O_y intrinsic Josephson junctions. Because of a large reduction of the Josephson penetration depth attributed to an atomic-scale thickness of the superconducting layers, a thermally activated depinning of Josephson vortices was found to dominate the behaviour of the switching current distribution for mesas with lateral dimensions between 10 × 10 and 40 × 40 µm². With decreasing lateral dimensions of the mesa, the measured switching current distribution was found to become much narrower than that in the thermally activated escape model. We argue that this behaviour is attributed to an increase in the retrapping events after an escape event.

The current–voltage characteristics of a micrometre bridge of intrinsic Josephson junctions under microwave irradiation are studied. The collective switching of the group of four junctions splits up as the AC signal amplitude is gradually increased. The switching current of the remaining group of junctions is increased with increasing radiation power. We consider that microwave irradiation injects an additional quasiparticle current into the Josephson junction array. We use ideas of breakdown of quasineutrality and quasiparticle charge imbalance in the superconducting layers and explain the experimental results by the competition between the 'current effect' and the effect of suppression of the switching current by irradiation.

Flux-flow cavity resonances in intrinsic Josephson junctions (IJJs) with long c-axis periodicity by artificial critical-current (J_c) modulation are studied numerically and theoretically. For an n-1–n-1–n-1–n IJJ system with n-layer high-J_c and one-layer low-J_c alternately stacked, numerical simulation confirms fluxon penetration only in the low-J_c junctions under proper low magnetic fields. The simulation also shows pronounced cavity-resonance steps in the I–V curves of the low-J_c junctions, meaning that fluxon dynamics can be generated under much lower magnetic fields, compared to the fields for usual IJJs with homogeneous J_c. A theoretical method for describing the flux-flow cavity-resonance properties is presented. The general disperse k–ω relationship shows that, at low-k regions, the critical-current-modulated junction system can be regarded as simple homogeneous stacked junctions with a new effective thickness and a new inductive coupling strength. For general-k cases, the cavity-resonant voltage steps on the I–V curves at various magnetic fields can be well indexed by integers, which means excellent agreement between the theoretical analysis and the numerical simulations.

A brief review of recent results on interlayer tunnelling spectroscopy of layered charge density wave (CDW) materials is presented, demonstrating the high capability of this method for studies of this electron condensed state. We discuss some features observed in comparison with high temperature superconductors (HTS).

The field dependence of the shear modulus c₆₆ in interlayer Josephson vortex systems in the ground state is investigated on the basis of the Lawrence–Doniach (LD) model. While c₆₆ was predicted to vanish exponentially as the external field increases for high fields in the London model, this quantity actually converges to a nonvanishing value for high fields in a simplified LD model without spatial dependence of the magnetic field and the amplitude of the superconducting order parameter. Such field independence of c₆₆ also holds when the spatial dependence of these quantities is taken into account. We also find that the shear instability field increases significantly when spatial dependence of the magnetic field is introduced, and that H_c2 becomes infinite for when spatial dependence of the amplitude of the superconducting order parameter is considered.

The predominant d-wave pairing symmetry in high temperature superconductors leads to an unconventional current–phase relation in Josephson junctions. This circumstance may induce new effects in the dynamics of dc SQUIDs. In this contribution we report on the measurements of the dependence of the SQUID Josephson current on the external magnetic field taken at very low temperatures, down to 20 mK. Different grain boundaries have been fabricated by using the biepitaxial and the bicrystal technique. Some of the effects which are induced by a nonsinusoidal current–phase relation can be clearly identified in the dynamics of the SQUIDs. The experimental data are also compared with theoretical simulations taking into account the inductance of the loop. The data show that, in specific conditions, a non-negligible inductance of the loop can induce effects similar to an unconventional current–phase relation, with a pronounced second harmonic sin(2φ) term. This fact has to be taken into account when designing d-wave SQUIDs for quantum circuitry.

We report an experimental observation of the macroscopic quantum tunnelling (MQT) in a d-wave high-temperature superconductor (HTSC) Bi₂Sr₂CaCu₂O_8+δ intrinsic Josephson junction (IJJs). It is well known that the current-biased Josephson tunnel junction provides an ideal stage for studying a variety of macroscopic quantum phenomena such as MQT. They have been studied and observed in low-temperature superconductor (LTSC) Josephson junctions since the early 1980s and have been established well by now. On the other hand, in the case of HTSC the d-wave pairing symmetry allows for dissipative quasiparticle excitations within the superconducting energy gap, which is expected to severely interfere with an observation of MQT. Contrary to this naive conception, our experimental results have explained that the effects of the nodal quasiparticles are not strong enough to obscure the observation of the MQT. Furthermore, we found that the MQT in IJJs was observed at approximately 1 K, which was ten times higher than that of LTSC Josephson junctions. This higher classical-to-quantum crossover temperature is due to their high plasma frequency. We also discuss the resonant activation of IJJs in the presence of microwave radiation.