Comment on "Density of states and reflectionless tunneling in an NS junction with a barrier

TL;DR

This paper discusses the density of states and conductance in superconductor/normal metal junctions with barriers, comparing different analytical approaches and interpretations of subgap conductance phenomena.

Contribution

It highlights the equivalence of different theoretical approaches to analyzing DOS and conductance in S/N junctions with barriers, clarifying the interpretation of subgap conductance.

Findings

DOS near the interface shows a pseudogap at low energies.

Subgap conductance arises from interference currents.

Different methods yield similar results but interpret the conductance differently.

Abstract

In a recent paper Schechter, Imry and Levinson (cond-mat/9709248) \cite{r1} analysed the density-of-states (DOS) and the conductance of a S/N junction with a barrier. They showed that the DOS in the N conductor near the barrier is strongly affected by the superconductor if the energy $\epsilon$ is small: $l_{n} \sqrt{\epsilon/D}{\ll} \Gamma {\ll} 1$, where $l_{n}$ is the mean free path, $D$ is the diffusion constant, and $\Gamma$ is the barrier transmittance. We would like to note that this problem was analysed in several papers with the use of different approaches. In particular, the author has calculated the DOS and the conductance of S/N structures with a barrier using quasiclassical matrix Green's function technique well developed in the theory of superconductivity \cite{r2}. It was shown that in an 1-d S/N structure a pseudogap appears in the N conductor near the S/N interface, and the DOS approaches it's normal value at energies $\epsilon$ exceeding an energy $\epsilon_{N}$ related to the interface transmittance; here $\epsilon_{N}=D/(2 R_{b} \sigma)^{2}$, $R_{b}$ is the interface resistance per unit area, and $\sigma$ is the specific conductivity of the N conductor. It was shown that peculiarities in the DOS at small energies lead to a subgap conductance at zero temperature. This subgap conductance is caused by a component of the current which is known in the theory of the Josephson effect as the interference current.Therefore, the results for the DOS and the conductance in Ref \cite{r1} are similar to the ones obtained earlier, but their interpretation of the subgap conductance differs from that given in Ref.\cite{r2} because they use another approach for the calculation of the conductance .