Interlayer Tunneling in High-Temperature Superconductors Beyond the Mean-Field Approximation

The interlayer tunneling in high-temperature superconductors has been reconsidered beyond the mean-field approximation. The modification of the quasiparticle spectrum originating from the momentum-conserving interlayer transportation of Cooper pairs has been taken into account exactly. The pronounced reduction of the superconducting transition temperature when compared to the mean-field solution can be observed. Our self-consistent Green's functions approach allows for incorporation of Coulomb correlation and gives support for the mixed s- and d-wave scenario of high-temperature superconductivity.     

Superconductivity Within the Pair-Tunneling Model Close to the Metal-Insulator Transition

We have considered the problem of s-wave and d-wave superconductivity in the two-layer Hubbard model close to the metal-insulator transition. To mimic the formation of the insulating gap, the Coulomb correlations have been taken into account within the Hubbard I approximation. The interlayer momentum-conserving Josephson tunneling between the layers has been included on the mean-field level. We demonstrate that the interlayer tunneling may contribute to the occurrence of mixed d + s wave symmetry of the superconducting state with a dominating d-wave component at a low concentration of holes. The problem of the validity of the pair-tunneling model is also briefly discussed.     

Superconductivity effects near the metal-insulator transition in granular indium films

The paper reports on an investigation of the electric resistance as a function of temperatureT, magnetic fieldH, and applied voltageV in granular indium films when approaching the metal-insulator transition (MIT) due to increased thickness of the oxide layers between granules. The dependences are shown to be governed atT5 K by competition of the hopping conductivity and the Josephson tunneling of electrons, sometimes giving rise to a resistance minimum inR(T) associated with superconductivity. It was also found that even when the intergranular Josephson tunneling is totally suppressed, transition of granules to the superconducting state influences essentially the dependencesR(T, H), changing the functional form ofR(T) and resulting in anomalously high negative magnetoresistance. This is shown to stem from the change of the character of activated electron tunneling as the granules become superconducting.     

Phase Diffusion and Suppression of the Supercurrent by Quantum-Mechanical Fluctuations of the Josephson Plasma at Small Superconducting Point Contacts

The RCSJ model of resistively and capacitively shunted Josephson junctions is used to describe superconducting point contacts over a wide range of resistances up to the metallic–tunneling transition. Their small dynamic capacitance of order C = 0.1 fF due to the point-contact geometry results in a huge plasma frequency. The critical current is then strongly suppressed and the contact resistance becomes finite because of quantum-mechanical zero-point fluctuations of the Josephson plasma and the rather large escape rate out of the zero-voltage state due to quantum tunneling. We test the predictions of the RCSJ model on the classical superconductors lead, indium, aluminum, and cadmium.     

STM tunneling spectroscopy on high Tc superconductors

STM tunneling spectroscopy has been performed on the bulk single crystals of BiSrCaCuO (BSCCO) and the epitaxial thin films of YBaCuO (YBCO) at cryogenic temperatures. The STM images and tunneling spectra observed on the (001) surfaces can be classified into three cases; 1) Atomic image is visible. However, the tunneling spectrum shows semiconducting or smeared superconducting gap structures, depending on the tip-sample distance. 2) Clear atomic image can not be obtained. But, the tunneling spectrum shows flat bottom region with quite low zero bias conductance. 3) Tunneling spectra demonstrate gapless behavior, independent of the tip-sample separation. These observations support the quasi-2D electronic picture in whichs-wave like 2D superconducting layers are coupled with each other through the Josephson effect.     

Superconducting tunneling without the tunneling Hamiltonian

The theory of superconducting tunneling is extended to treat superconducting junctions with arbitrarily thin, but structureless tunnel barriers. An exact expression for the tunneling current is obtained, using standard, many-body, nonequilibrium Green's function techniques, assuming Fermi distributions in each electrode. The tunneling current result agrees with the recent theory of Blonder, Tinkham, and Klapwijk, but extends their results to treat strong coupling superconductors, proximity effect tunneling, and the effects of tunneling angle. Results for the Josephson critical current in S' INS (superconductor S', insulator I, metal N, superconductor S) junctions, where NS is a proximity effect double layer, are presented for barrier thicknesses ranging from zero to barrier thicknesses for which the tunneling Hamiltonian approach is correct, and for varying N metal thicknesses. Results forI-V curves are presented for normal metal (M)-INS junctions for a similar range of barrier thicknesses and N metal thicknesses. It is shown that the tunneling currentI is the sum of a supercurrentI _SUP carried solely by Cooper pairs through S, and a quasiparticle currentI _QP carried solely by quasiparticles. The influence of leakage on phonon structure observed on tunneling into strong coupling superconductors is described. The nonoscillating portion of the Josephson current is plotted as a function of voltage for the S' INS junction in the tunneling Hamiltonian limit.     

Effect of interlayer interaction in high-Tc cuprate superconductors

We have studied the role of interlayer attractive interaction in a high-T _c system having two layers per unit cell. The single band two-layer tight binding model Hamiltonian is considered and the double time Green's function technique is applied within the mean field approximation. The expressions for the hole density, transition temperature, and intra- and interlayer order parameters are obtained which are found to be dependent on the interlayer interaction and other parameters appearing in the Hamiltonian. The numerical analysis shows that the coupling of the charge carriers (holes) between the layers provides better conditions for the stabilization of long-range order and high superconducting transition temperature in layered superconductors. It is also observed that superconductivity is confined to a narrow region of hole concentration and the single particle tunneling suppresses the transition temperature.     

Resonant tunneling and perpendicular conduction in cuprate conductors with varying O-content

Anisotropy is inherent to layered cuprates with conduction mainly confined to the CuO₂-planes, claimed to be the source of superconductivity. Resonant tunnel exchange for conduction parallel and perpendicular to the CuO₂-planes shows different normal and superconducting properties by charging energies and localizations at the in-plane perturbations being atomic-like and between the CuO₂-planes, being extended. By overdoping the wave function overlap in perpendicular direction via the extended states grows, especially in the superconducting state. The counteraction of overlap and charging energies yield activated resonant tunneling, i.e. the pseudo gap, in the normal state and Josephson tunneling in the superconducting state.     

The effect of alternating current on the thermal activation threshold of the tunnel Josephson junctions

The process of thermal activation in the tunnel Josephson junctions simultaneously carrying both constant (dc) and alternating (ac) currents has been studied. The presence of the ac component leads to a decrease in the potential barrier for a metastable state of the Josephson junction. The thermal activation threshold is expressed as a function of the ac current amplitude. The results agree with the data of recent experiments on the statistics of switching from a superconducting to resistive state in the Josephson tunneling junctions.     

Single-electron and Cooper-pair tunneling in ultrasmall Josephson junctions. Coulomb and environmental effects

We study the I-V curve of a small capacitance Josephson tunnel junction with a zero subgap conductance. In the limit of large external impedance and at low temperature, single electron tunneling across the junction is suppressed for eV < 2 + E_c due to a combination of superconducting and Coulomb gaps and the process of Cooper pair tunneling (CPT) plays the main role. For E _c , 2 Coulomb interaction between electrons of a tunneling Cooper pair strongly modifies the effective Josephson coupling energy and the CPT current can substantially deviate from its standard value. Very close to the point eV - 2 the effective tunneling time of a Cooper pair becomes very large and the CPT process is not adiabatic.     

Superconducting properties of Pb/Ag multilayers

The electrical resistivity, ac susceptibility, critical current density, and Josephson tunneling of Pb/Ag multilayers have been measured in wide temperature ranges in order to study the proximity effect. A resistivity drop was found to occur atT _c of Pb in versusT measurement and, at low temperature, the multilayers show proximity effect. The I-V characteristic of the multilayer shows voltage steps, indicating a resistive state has occurred in the sample. The superconducting properties of the multilayer were analyzed with the bilayer theory of the proximity effect.     

The superconducting transition temperature of multilayered superconductors. The frustratedXY-Josephson model

The superconducting transition temperature of multilayered superconducting structures of the RVB theory for the S-N(D)-S type is defined taking into account the resonance pair “tunneling” between superconducting layers. The Josephson array defectivity is considered with the frustration parameters.     

The superconducting transition temperature of multilayer superconductors: The frustratedXY-Josephson model

The superconducting transition temperature of multilayered superconducting structures of the S-N(D)-S type in the RVB theory is defined taking into account the resonance pair “tunneling” between superconducting layers. The Josephson array defectivity is considered with the frustration parameters.     

Importance of out-of-plane dispersion of the excitation spectrum of superconducting bilayers with Josephson coupling

We study the effect of Josephson coupling between adjacent superconducting layers on the BCS energy spectrum. We find that the interference between the gap functions of two layers can lead to vanishing condensation energy for perpendicular momenta corresponding to the formation of standing waves. We therefore predict a conventional energy spectrum for large interlayer spacings, if the gap of the single layers has no nodes, and in all cases a gapless spectrum for small spacings. Within the experimental error, our numerical results account for the low-temperature dependence of the penetration depth reported in Nd_1.85Ce_0.15CuO₄ and YBa₂Cu₃O_6.9.     

Fluctuations and the superconducting phase transition: II. Onset of Josephson tunneling and paraconductivity of a junction

When one metallic film of a tunneling junction is in the superconducting state but the other is above its transition temperature, fluctuations in the pair field of the second film cause instantaneous Josephson currents to flow. Application of the Kubo formula to these current fluctuations yields a conductivity with a strong temperature dependence, tending to infinity at the transition. The numerical magnitude of this "paraconductivity" is sufficiently large to be observable for junctions of very low normal resistance (and may possibly be compared with some recent measurements of Lipsonet al.). High-frequency studies would determine directly the pair relaxation rate. An experimental advantage of tunneling paraconductivity is that it is not sensitive to the electron mean free path and therefore does not require amorphous films.This work has been supported in part by the Air Force Office of Scientific Research and by the Office of Naval Research.National Science Foundation Senior Postdoctoral Fellow.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Tunneling Photocurrent Assisted by Interlayer Excitons in Staggered van der Waals Hetero‐Bilayers

Vertically stacked van der Waals (vdW) heterostructures have been suggested as a robust platform for studying interfacial phenomena and related electric/optoelectronic devices. While the interlayer Coulomb interaction mediated by the vdW coupling has been extensively studied for carrier recombination processes in a diode transport, its correlation with the interlayer tunneling transport has not been elucidated. Here, a contrast is reported between tunneling and drift photocurrents tailored by the interlayer coupling strength in MoSe₂/MoS₂ hetero‐bilayers (HBs). The interfacial coupling modulated by thermal annealing is identified by the interlayer phonon coupling in Raman spectra and the emerging interlayer exciton peak in photoluminescence spectra. In strongly coupled HBs, positive photocurrents are observed owing to the inelastic band‐to‐band tunneling assisted by interlayer excitons that prevail over exciton recombinations. By contrast, weakly coupled HBs exhibit a negative photovoltaic diode behavior, manifested as a drift current without interlayer excitonic emissions. This study sheds light on tailoring the tunneling transport for numerous optoelectronic HB devices.     

Superconducting tunneling without the tunneling Hamiltonian. II. Subgap harmonic structure

The theory of superconducting tunneling without the tunneling Hamiltonian is extended to treat superconductor/insulator/superconductor junctions in which the transmission coefficient of the insulating barrier approaches unity. The solution for the current in such junctions is obtained by solving the problem of a particle hopping in a one-dimensional lattice of sites, with forward and reverse transfer integrals that depend on the site. The results are applied to the problem of subgap harmonic structure in superconducting tunneling. The time-dependent current at finite voltage through a junction exhibiting subgap structure is found to have terms that oscillate at all integer multiples of the Josephson frequency,n(2eV/). The amplitudes of these new, and as yet unmeasured, ac current contributions as a function of voltage are predicted.     

Tunneling and Phase-Sensitive Studies of the Pairing Symmetry in Sr2RuO4

Results obtained from several tunneling experiments on the pairing symmetry in Sr₂RuO₄ are reported. A normal surface layer was found to be present on the ab face of single-crystalline Sr₂RuO₄ in the c-axis tunnel junctions. Measurements in the in-plane junctions, however, revealed features suggesting a suppressed, but non-zero superconducting gap and Andreev bound states (ABSs) associated only with an unconventional superconductor. Josephson coupling between a conventional s-wave superconductor and Sr₂RuO₄ has been used to probe the pairing symmetry in the latter, through both the selection rule and the phase sensitive experiments. All results indicate that Sr₂RuO₄ is unconventional, most likely spin-triplet superconductor. Finally, some recent studies of several newly-characterized ruthenates are reviewed.     

c-axis Superfluid Response and Quasiparticle Conductivity in Bi2Sr2CaCu2O8+δ and Bi2Sr2CuO6+δ

Josephson plasma resonance for underdoped Bi ₂ Sr ₂ CaCu ₂ O ₈₊ and Bi ₂ Sr ₂ CuO ₆₊ have been measured by sweeping the microwave, frequency continuously. The resonance enables us to determine the superfluid density and quasiparticle conductivity in the c-axis accurately. We show that the. superfluid response and the low energy excitations out of the condensate in the c-axis of these materials are very different from those in the ordinary Josephson multilayer tunnel junctions. The Josephson coupling energy in single layer Bi ₂ Sr ₂ CuO ₆₊ is more than 5000 times smaller than is predicted in interlayer tunneling model.