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.

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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.