Angle dependence of Andreev scattering at semiconductor-superconductor interfaces

TL;DR

This paper investigates how the angle of incidence affects Andreev scattering at semiconductor-superconductor interfaces, revealing angle-dependent suppression of Andreev reflection and the existence of a critical angle due to Fermi velocity mismatch.

Contribution

It generalizes the one-dimensional BTK theory to higher dimensions, incorporating angle dependence and Fermi velocity mismatch effects on Andreev scattering.

Findings

Increased parallel momentum suppresses Andreev reflection.

Fermi velocity mismatch leads to Snell's law-like angle relations.

Lower excess current in 2D and 3D interfaces compared to 1D models.

Abstract

We study the angle dependence of the Andreev scattering at a semiconductor-superconductor interface, generalizing the one-dimensional theory of Blonder, Tinkham and Klapwijk. An increase of the momentum parallel to the interface leads to suppression of the probability of Andreev reflection and increase of the probability of normal reflection. We show that in the presence of a Fermi velocity mismatch between the semiconductor and the superconductor the angles of incidence and transmission are related according to the well-known Snell's law in optics. As a consequence there is a critical angle of incidence above which only normal reflection exists. For two and three-dimensional interfaces a lower excess current compared to ballistic transport with perpendicular incidence is found. Thus, the one-dimensional BTK model overestimates the barrier strength for two and three-dimensional interfaces.