Methods of quasiclassical Green’s functions in the theory of transport phenomena in superconducting mesoscopic structures

Abstract

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.

Anomalous transport in normal-superconducting and ferromagnetic-superconducting nanostructures

“…This non-monotonic behaviour has been observed both in very short S/N contacts [9] and in longer mesoscopic S/N structures [10][11][12]21]. In ref [6] it was noted that the conductance δG = G − G n consists of two contributions. The first, δG DOS , is negative due to a proximity effect induced decrease in the density of states (DOS) of the normal wire which makes contact with a superconducting strip [13].…”

“…In this case Nazarov and Stoof [4] (also see [5][6][7]) argued that the temperature dependence of the conductance G has a similar non-monotonic behaviour with a maximum at a temperature comparable with the Thouless energy, while simultaniously Volkov, Allsopp and Lambert [8] predicted that the voltage dependence of the conductance in an S/N mesoscopic structure (Andreev interferometer) has a similar form with a maximum at eV m ≈ ǫ T h . This non-monotonic behaviour has been observed both in very short S/N contacts [9] and in longer mesoscopic S/N structures [10][11][12]21].…”

“…Although they differ slightly from each other, in the limit l 1 << 1 (l 1 = L 1 /L) the formulae for the conductances of these systems are identical. We assume the metals are diffusive and employ the well developed quasiclassical Green's function technique (see for example [15]) which has been widely used for studying transport phenomena in S/N mesoscopic structures [2][3][4][5][6]8,[16][17][18][19]7,20,21]. Using the Keldysh formalism, the conductance variation of the structure shown in Fig.…”

“…Eq. (2) can be solved numerically [4,5], and in some limiting cases analytically [3][4][5][6]8,[16][17][18][19]7,20,21].…”

Properties of superconductor–Luttinger-liquid hybrid systems

“…Thus, quantum ballistic electron propagation dominates in small-scale Sc systems. The interplay between phase-coherent electron propagation in Sc and macroscopic phase coherence in S gives rise to interesting new physics [6][7][8][9].…”