Magnetic focusing in normal-superconductor hybrid systems: a semiclassical analysis

TL;DR

This paper investigates electron-hole focusing in normal-superconductor systems, deriving a semiclassical conductance formula that aligns well with quantum results and classical dynamics, revealing oscillations and conductance suppression at different magnetic fields.

Contribution

It introduces a semiclassical approach to analyze electron-hole focusing and conductance in normal-superconductor systems, bridging quantum and classical perspectives.

Findings

Semiclassical conductance matches quantum calculations.

Oscillations in conductance due to Andreev reflection at low fields.

Conductance approaches zero at higher magnetic fields.

Abstract

We study a transverse electron-hole focusing effect in a normal-superconductor system. The spectrum of the quasiparticles is calculated both quantum mechanically and in semiclassical approximation, showing an excellent agreement. A semiclassical conductance formula is derived which takes into account the effect of electron-like as well as hole-like quasiparticles. At low magnetic field the semiclassical conductance shows characteristic oscillations due to the Andreev reflection, while at higher fields it goes to zero. These findigs are in line with the results of previous quantum calculations and with the expectations based on the classical dynamics of the quasiparticles.