Thermo-Coulomb effects in mesoscopic tunnel junctions

We present a study of the thermoelectric effect in tunnel junctions. In particular we calculate the thermopower coefficientS and the Peltier coefficient . For macroscopic junctions we demonstrate the sensitivity ofS and to the structure of the density of states. For mesoscopic junctions we show that Coulomb effects modify the ordinary Onsager picture and the relation =TS. The coefficientsS and are found to be very sensitive to the coupling of the junctions to the external world. We analyze measurements of the thermopower in granular films in terms of the thermo-Coulomb effects. We comment on the relevance of these effects to scanning tunneling microscope measurements.     

Density of states in a mesoscopic SNS junction

The semiclassical theory of proximity effects predicts a gap E _g～?D/L ² in the excitation spectrum of a long diffusive superconductor/normal-metal/superconductor (SNS) junction. Mesoscopic fluctuations lead to anomalously localized states in the normal part of the junction.As a result, a nonzero, yet exponentially small, density of states (DOS) appears at energies below E _g. In the framework of the supermatrix nonlinear σ model, these prelocalized states are due to the instanton configurations with broken supersymmetry. The exact result for the DOS near the semiclassical threshold is found, provided the dimensionless conductance of the normal part G _N is large. The case of poorly transparent interfaces between the normal and superconductive regions is also considered. In this limit, the total number of subgap states may be large.     

Nonequilibrium mesoscopic transport: a genealogy

Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and gain even greater and more explicit experimental meaning in the passage to atomic-sized devices. We review their genesis, their theoretical context, and their governing role in the electronic response of meso- and nanoscopic systems.     

Thermoelectric ac Josephson effect in SNS junctions

It was experimentally evidenced, that Josephson radiation from an SNS junction exists, when a heat flow across the junction exceeds a critical value P_c. The ac component of the thermoelectric voltage was observed directly. The heat-flux-voltage characteristic of a TaCuTa junction showed steps of constant voltage, when the junction was irradiated by an external electromagnetic field at frequenct ～ 10² Hz.     

Critical current in planar SNS Josephson junctions

Specific features of the proximity effect and Josephson behavior of submicron planar SNS junctions fabricated by electron beam lithography and shadow evaporation have been studied experimentally and theoretically. The critical current of the junctions has been found to drastically increase with a decrease in temperature, which is associated with a change in the effective size of the weak link owing to the additional SN interface.     

Resistance of superconductor-normal-metal-superconductor (SNS) junctions

It is shown that the conductance of a superconductor-normal-metal-superconductor (SNS) junction can exhibit a significant dependence on the phase of the superconducting order parameter in the situation where the size of the normal region of the junction is much larger than the normal-metal coherence length, so that the critical current of the junction is exponentially small. The period of the conductance oscillations as a function of the phase can be equal to π or 2π, depending on the parameters of the system. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 347–352 (25 February 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Magnetic interference patterns and vortices in diffusive SNS junctions

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonic decay when the width of the normal wire is smaller than the magnetic length xi(H)=square root Phi(0)/H, where H is the magnetic field and Phi(0) the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how this structure is manifested in the local density of states.     

Phase-sensitive reentrance into the normal state of mesoscopic SNS structures

Normal (N) metallic (Ag) mesoscopic conductors with two superconducting (S) faces (Al), arranged mirror-symmetrically relative to the streamlines of the current, periodically switch into the normal state as the superconducting phase difference Δϕ between the NS boundaries approaches the values Δϕ =(2n+1)π, n=0,1,2,..., irrespective of temperature and applied voltage. For Δϕ =2nπ and low applied voltages the conductance passes through a maximum and approaches the normal value as temperature decreases (reentrance). As the voltage subsequently increases, the conductance increases and passes through a maximum. As the phase difference moves away from the values Δϕ=2nπ, the maxima shift in the direction of low temperatures and voltages. The latter result shows unequivocally that in our metal structures it is necessary to take into account the next-order corrections to the “weak” proximity effect approximation. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 489–494 (10 April 1998)     

Magnetic field dependence of JC in SNS junctions

Critical currents for triple layer superconducting-normal metal-superconducting (SNS) junctions have been measured with the normal metal in the thick-clean limit in order to determine the spatial variation of the order paremeter as a function of magnetic field (H). Critical currents fall exponentially with H as might be expected if the decay length, K^-1_N, varies linearly with H. The diffusivity, D_N, derived from the measured depairing parameter, α=D_NeH/c, agrees with the diffusivity determined from resistivity measurements.     

Nonequilibrium Zeeman splitting in quantum transport through nanoscale junctions

We calculate the differential conductance G(V) through a quantum dot in an applied magnetic field. We use a Keldysh conserving approximation for weakly correlated and the scattering-states numerical renormalization group for the intermediate and strongly correlated regime out of equilibrium. In the weakly correlated regime, the Zeeman splitting observable in G(V) strongly depends on the asymmetry of the device. In contrast, in the strongly correlated regime the position Δ(K) of the Zeeman-split zero-bias anomaly is almost independent of such asymmetries and of the order of the Zeeman energy Δ(0). We find a crossover from the purely spin-fluctuation driven Kondo regime at small magnetic fields with Δ(K)<Δ(0) to a regime at large fields where the contribution of charge fluctuations induces larger splittings with Δ(K)>Δ(0) as it was observed in recent experiments.     

New model for systems of mesoscopic Josephson junctions

Quantum fluctuations of the phases of the order parameter in two-dimensional arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores containing superfluid helium, or Josephson junctions in which the average number of particles n ₀ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate operators is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for n ₀<5 and U<J (U is the characteristic interaction energy of the particles per granule and J is the Josephson coupling constant). Re-entrant superconductivity phenomena are discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 649–654 (25 November 1997)     

Subgap anomaly and above-energy-gap structure in chains of diffusive SNS junctions

We present the results of low-temperature transport measurements on chains of superconductor-normal constriction-superconductor (SNS) junctions fabricated on the basis of superconducting PtSi film. A comparative study of the properties of the chains, consisting of 3 and 20 SNS junctions in series, and single SNS junctions reveals essential distinctions in the behavior of the current-voltage characteristics of the systems: (i) a gradual decrease of the effective suppression voltage for the excess conductivity observed at zero bias as the quantity of the SNS junctions increases; (ii) a rich fine structure on the dependences dV/dI-V at dc bias voltages higher than the superconducting gap and corresponding to some multiples of 2Δ/e. A model explaining this above-energy-gap structure based on the energy relaxation of electrons via Cooper-pair-breaking in the superconducting island connecting normal metal electrodes is proposed.     

Nonequilibrium noise as a probe of the Kondo effect in mesoscopic wires

We study the nonequilibrium noise in mesoscopic diffusive wires hosting magnetic impurities. We find that the shot-noise to current ratio develops a peak at intermediate source-drain biases of the order of the Kondo temperature. The enhanced impurity contribution at intermediate biases is also manifested in the effective distribution. The predicted peak represents an increased inelastic scattering rate at the nonequilibrium Kondo crossover.     

Phase coherence,quantization, and thermal fluctuations in SNS junctions

Quasiparticles in the bound and continuum states of superconducting- normal-superconducting junctions are scattered by thermal fluctuations. The scattering rates are computed as functions of temperature and normal layer thickness. Phase coherence of the pair potential is broken, if more than half of the quasiparticles in the continuum states are scattered before crossing of the N-region once. For the corresponding critical quasiparticle life-time τ_Kc (coherence time) the r.m.s. fluctuation of the phase difference $\text{〈}\text{χ}{}^2\text{(}\text{τ}{}_{\mathrm{Kc}}\text{)〉}\text{1}\text{2}$ is of the order of π. Except at very low temperatures the bound states are considerably more stable against thermal fluctuations than the continuum states so that even in the absence of phase coherence the size-dependent quantization of the Andreev spectrum exists for sufficiently large momenta normal to the layer boundaries.