Andreev bound states and self-consistent gap functions in clean layered superconductor/normal metal systems with finite transverse width

Abstract

Andreev bound states in clean, ballistic SNS and SNSNS junctions are calculated exactly and by using the Andreev approximation ͑AA͒. The AA appears to break down for junctions with transverse dimensions chosen such that the motion in the longitudinal direction is very slow. The doubly degenerate states typical for the traveling waves found in the AA are replaced by two standing waves in the exact treatment and the degeneracy is lifted. A multiple-scattering Green's function formalism is used, from which the states are found through the local density of states. The scattering by the interfaces in any layered system of ballistic normal metals and clean superconducting materials is taken into account exactly. The formalism allows, in addition, for a selfconsistent determination of the gap function. In the numerical calculations the pairing coupling constant for aluminum is used. Various features of the proximity effect are shown.

Andreev states, supercurrents and interface effects in clean superconducting/normal metal multilayers

“…18. In order to compare multilayer results with publicated SNS results 5,7 , we calculated the LDOS inside the N and S layers of a multilayer with d N = d S = 4000 Bohr. This is shown in Fig.…”

“…Ishii [2] and Furusaki et al [3,4] Recently [5], a powerful Green function formalism was published which unified earlier formulations [1][2][3][4] and improved upon them. First applications were made for NS, SNS, and SNSNS systems [5][6][7]. An important feature of these calculations was that the systems were chosen to have a finite transverse width and they were focused on particular phenomena which occur at specially chosen transverse widths.…”

The electronic structure of normal metal–superconductor bilayers

“…This point has been discussed previously [15] in the context of superconductor-normal metalsuperconductor junctions, where it was shown that normal reflections can dominate the Andreev reflection process. Recently, Andreev bound states have also been numerically calculated [16] exactly and self-consistently for clean bulk N/S junctions. It was found that the quasiclassical approximation fails for certain transverse junction widths.…”

Magnetic susceptibility of Dirac fermions, Bi-Sb alloys, interacting Bloch fermions, dilute nonmagnetic alloys, and Kondo alloys

“…Topological superconductors are simply the analogue of topological insulators. Whereas, topological insulators (TI) have a bulk band-gap with odd number of relativistic Dirac fermions and gapless modes on the surface, topological superconductors (TSC) are certain type of full superconducting gap TSC in the bulk, but due to the inherent particle-hole symmetry, have gapless modes of chargeless Majorana 'edge' states, also associated with Andreev bound state (ABS) 29,30 on its boundaries, interfaces (e.g. interface between topological insulators and superconductors), and defects, supported by the bulk topological invariants.…”