We analysed the electron-hole or, in another words, branch imbalance (BI) and the related electric potential V imb which may arise in a mesoscopic superconductor/normal metal (S/N) structure under non-equilibrium conditions in the presence of a supercurrent. Non-equilibrium conditions can be created in different ways: a) a quasiparticle current flowing between the N reservoirs; b) a temperature gradient between the N reservoirs and no quasiparticle current. It is shown that the voltage V imb oscillates with the phase difference ϕ. In a cross-geometry structure the voltage V imb arises in the vertical branch and affects the conditions for a transition into the π−state.A few decades ago a great deal of interest was paid to the study of effects related to the so called branch imbalance (BI) (see Refs. [1,2] and for example the reviews [3,4]). The BI implies that populations of the electron-like and hole-like branches of the excitation spectrum in a superconductor or a normal metal are different. For example, the BI may arise in a superconductor near the S/N interface if a current flows through this interface and the temperature is close to T c . The conversion of the quasiparticle current j Q into the condensate current j S occurs over a rather long length λ Q called a BI relaxation length. Over this length populations of the electron-like and hole-like branches of the energy spectrum differ from each other. The difference between these populations is characterized by the distribution function f − = −(n ↑ − p ↓ ); the function n ↑ is the distribution function of the electron-like excitations and p ↓ (ǫ) = 1−n ↓ (−ǫ) is the distribution function of the hole-like excitations. In the considered case of a spin-independent interaction one has n ↑ = n ↓ and p ↑ = p ↓ . One can show that the function f − differs from zero if divj Q = 0. The non-zero distribution function f − leads to the appearance of an electric potential V imb in a superconductor (or in a normal metal) which can be expressed in terms of the function f − (see below). The BI may also arise in a bulk superconductor. For example, if longitudinal collective oscillations with a finite wave vector q are excited in the superconductor, the BI arises because in this case divj Q = iqj Q = 0 . When these modes are excited (they are weakly damped only near T c ), the quasiparticle current j Q oscillates in a counter phase with the condensate current j S , so that the total current remains equal to zero. These oscillations have been observed experimentally by Carlson and Goldman (Carlson-Goldman mode) [5] and have been explained theoretically in Refs. [6,7]. Another example of a system, in which the BI arises, is a uniform superconducting film in the presence of a temperature gradient ∇T and a condensate flow. It was established experimentally [8] and theoretically [9,10,11] that in this case the BI has a magnitude which is proportional to v s ∇T , where v s is the condensate velocity.Recently there has been growing interest in the study of transport properties of S/...

The detector response of YBa2Cu3O7−x Josephson grain-boundary junctions to monochromatic radiation with the frequency f in the range from 60 GHz to 4 THz has been studied. Frequency-selective odd-symmetric resonances in the responses ΔI(V) of these junctions to radiation with different frequencies f have been observed near the voltages V=hf/2e in almost a decade of spectral range for any operating temperature in the range from 30 to 85 K. The spectral range of the selective detection has scaled with the IcRn product of the Josephson junction, reaching the range of 0.16–3.1 THz for a IcRn product of 1.5 mV. A resolving power δf/f of around 10−3 has been demonstrated in the selective detection by Josephson junctions. The high-frequency falldown of the amplitude of the selective response has been found to be proportional to exp[−P/P0], where P=(hf/2e)2/Rn is the power dissipated in the junction at the resonance and P0 is a characteristic power level. The values of P0 for our junctions were around 20 μW at 34 K and 2 μW at 78 K.

No abstract

We consider a simple phenomenological model of a semiconductor with absolute negative conductance in a magnetic field. We find the form of the domains of the electric field and current which arise as a result of an instability of a uniform state. We show that in both Corbino disc and Hall bar samples the residual conductance and resistance are negative and exponentially small; they decrease exponentially with increasing length Lx,y.

A short introduction to the theory of matrix quasiclassical Green's functions is given and possible applications of this theory to transport properties of mesoscopic superconducting-normal metal (S/N) structures are considered. We discuss a simplified version of these equations in the diffusive regime and in the case of a weak proximity effect. These equations are used for the calculation of the conductance of different S/N structures and for analysis of kinetic phenomena in these structures. We discuss the subgap conductance measured in SIN tunnel junctions and the mechanism of a nonmonotonic dependence of the conductance of a N wire on temperature T and voltage V , observed in an S/N structure.Long-range, phase-coherent effects are studied in a 4-terminal S/N/S structure under conditions when the Josephson critical current is negligible (the distance between superconductors is much larger then the coherence length in the normal wire). It is shown that the Josephson effects may be observed in this system if a current I, in addition to a current I 1 in the S/N/S circuit, flows through the N electrode.

We consider a mesoscopic four-terminal superconductor/normal metal (S/N) structure in the presence of a temperature gradient along the N wire. A thermoemf arises in this system even in the absence of the thermoelectric quasiparticle current if the phase difference between the superconductors is not zero. We show that the thermoemf is not small in the case of a negligible Josephson coupling between two superconductors. It is also shown that the thermoelectric voltage has two maxima: one at a low temperature and another at a temperature close to the critical temperature. The obtained temperature dependence of the thermoemf describes qualitatively experimental data.

The application of Hilbert-transform spectroscopy for the measurement of high-harmonic content of the radiation from a frequency multiplier has been demonstrated in the spectral range from 60 to 450 GHz. YBa2Cu3O7−x grain-boundary Josephson junctions made on (110) NdGaO3 bicrystal substrates have been used in these experiments. The internal Josephson radiation of the junctions reveals a Lorentzian shape due to thermal noise broadening. The possibility to obtain a spectral resolution as low as 280 MHz (∼0.01 cm −1) has been shown with a Josephson junction operating at liquid-nitrogen temperature.

Using an approach based on quasiclassical Green's functions we present a theoretical study of transport in mesoscopic S/N structures in the diffusive limit. The subgap conductance in S/N structures with barriers (zero bias and finite bias anomalies) are discused. We also analyse the temperature dependence of the conductance variation δS(T ) for a Andreev interferometer. We show that besides the well know low temperature maximum a second maximum near Tc may appear. We present the results of studies on the Josephson effect in 4 terminal S/N/S contacts and on the possible sign reversal of the Josephson critical current. IntroductionThe theory describing non-equilibrium transport in superconductors was developed 20 years ago (see, for example [1]) and has been used to explain phenomena such as viscous flux flow, Josephson effects in superconducting weak links and the passage of the current over the interface between a superconductor and a normal metal (an S/N interface). Technological advances achieved in the last decade have enabled the fabrication of mesoscopic structures where the dimensions are less than the energy relaxation length and with well defined physical properties. In mesoscopic systems phase coherence is maintained and the distribution of quasiparticles may differ significantlty from equilibrium. Experiments on these structures have revealed a number of new effects such as, subgap conductance in SIN junctions (where I is an insulating layer), the oscillatory dependence of the conductance in S/N structures containing normal metal or superconducting loops, the non-monotonic dependence of the N film conductance on the temperature and voltage in S/N structures; long-range, phase-coherent effects, change of sign of the Josephson critical current in 4-terminal S/N/S structures when an additional current is driven through the N film. Although it is only recently that most of these effects have been explained using a non-equilibrium theory developed at the end of the 1970's (see [2,3]). One method for studying these effects (ballistic systems in particular) is based on the Bogolyubov-de Gennes equations and the Landauer formula for the conductances [2,3]. In this paper we use another approach based on a microscopic, quasiclassical Green's function technique, which has been successfully applied to systems with a small mean free path (i.e. diffusive regime), to analyse these effects. The method of matrix, quasiclassical Green's functions is a convenient and powerful method for studying transport in mesoscopic S/N structures [4]. The quasiclassical approximation means that all the Green's functions are spatially averaged over distances of order of the Fermi wave length p