Crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions

Abstract

Andreev levels deplete energy states above the superconductive gap, which leads to the peculiar nonmonotonous crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions. This effect is especially pronounced in the case when the normal metal bridge length L is small compared to the superconductive coherence length ξ. Remarkable property of the crossover function is that it vanishes not only at the proximity induced gap ǫ g but also at the superconductive gap ∆. Analytical expressions for the density of states at the both gap edges, as well as general structure of the crossover are discussed. PACS numbers: 74.45.+c Experimental advances in probing systems at the mesoscopic scale 1,2,3,4,5 revived interest to the proximity related problems in superconductor -normal metal (SN) heterostructures. 6 The most simple physical quantity reflecting proximity effect is the local density of states (LDOS) ρ(ǫ, r), which can be measured in any spatial point r at given energy ǫ using scanning tunneling microscopy. The effects of superconductive correlations on the spectrum of a normal metal are especially dramatic in restricted geometries. For example, in the case of superconductor-normal metal-superconductor (SNS) junction, proximity effect induces an energy gap ǫ g in excitation spectrum of a normal metal with the square root singularity ρ(ǫ, r) ∝ ǫ/ǫ g − 1 in the density of states just above the threshold ǫ − ǫ g ≪ ǫ g Ref. 7,8,9,10,11,12 (here and in what follows, ρ will be measured in units of the bare normal metal density of states ν at Fermi energy). The most recent theoretical interest was devoted either to mesoscopic 13,14,16,17 or quantum 18,19,20,21 fluctuation effects on top of mean-field results 7,8,9,10,11,12 that smear hard gap below ǫ g and lead to the so called subgap tail states with nonvanishing ρ ∝ exp − g(1 − ǫ/ǫ g ) (6−d)/4 at ǫ g − ǫ ǫ g , where g is the dimensionless normal wire conductance and d is the effective system dimensionality. The latter is essentially a nonperturbative result that requires instantonlike approach within σmodel 19,20 or relies on methods of random matrix theory. 16,18 Surprisingly, after all of these advances, there is something interesting to discuss about proximity induced properties of the SNS junctions even at the level of quasiclassical approximation by employing Usadel equations. 22 The purpose of this work is to point out a subtle feature of the crossover in the local density of states of mesoscopic SNS junctions. The latter was seen in some early and recent studies, 8,11,12,14,15 however, neither emphasized nor theoretically addressed.To this end, consider normal wire (N) of length L and width W located between two superconductive electrodes (S). In what follows, we concentrate on diffusive quasi-onedimensional geometry and the short wire limit L ≪ ξ, where ξ = √ D S /∆ is superconductive coherence length, with D S as the diffusion coefficient in the superconductor and ∆ as the energy gap (hereafter, = 1). The center of th...

Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types

“…At first glance, this seems to disagree with Ref. [26] but is possibly due to differences in the considered geometries. The lowest Fig.…”

“Smile” Gap in the Density of States of a Cavity between Superconductors

“…Mesoscopic fluctuations of the DOS [23,24] are small provided G ≫ G Q . It looks like everything is understood, perhaps except a small dip or peak in the DOS just at the gap edge for the diffusive case, which has been seen in [3,5,[25][26][27][28], but never attracted proper attention.In this Letter, we demonstrate that the appearance of a secondary gap, in addition to the well-known gap ∼E Th in the DOS around the Fermi level, is a generic feature of S-N-S structure containing high-transmission S-N contacts. In the case of a chaotic cavity with two identical ballistic contacts, the secondary gap exists for any E Th > 0.68Δ and vanishes as Δ 3 =E…”

“…Mesoscopic fluctuations of the DOS [23,24] are small provided G ≫ G Q . It looks like everything is understood, perhaps except a small dip or peak in the DOS just at the gap edge for the diffusive case, which has been seen in [3,5,[25][26][27][28], but never attracted proper attention.…”

“…Unlike the bridge geometry of [27], we assume that, for the geometry we consider, the spatial dependence of the Green's functions is not relevant. Therefore, we can make use of the discretized form of the method-the so-called quantum circuit theory [30,31].…”

Scanning tunneling microscopy of superconducting topological surface states inBi2Se3

“…[39] As a first approach we have considered the diffusive limit that should be relevant to a part of the proximity effect governed by the trivial surface states. In complete analogy to previously studied mesoscopic superconductor-normal proximity junctions [41,42] we solved the standard Usadel equation for a circular geometry describing a superconducting island of radius R surrounded by an infinite normal system. Within this formalism the proximity effect is described by the semiclassical Green's function G(x, ω) = cos[θ(x, ω)] of position and energy that in the normal region obeys the nonlinear equation…”