Magnetic-field dependence of transport in normal and Andreev billiards: a classical interpretation to the averaged quantum behavior

TL;DR

This study compares quantum and classical transport in normal and Andreev billiards under magnetic fields, showing classical trajectories can explain quantum behavior, aiding experimental design.

Contribution

It demonstrates that classical dynamics can accurately describe quantum transport properties in billiards across varying magnetic fields.

Findings

Classical and quantum transport coefficients agree well across all magnetic fields.

Transport behavior can be explained by classical trajectories, even with quantum fluctuations.

Non-monotonic magnetoconductance behavior is linked to classical phase space changes.

Abstract

We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field $B$. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall description of the non-monotonic behavior of the average magnetoconductance in terms of the corresponding classical trajectories, thus, establishing a basic tool useful in the design and analysis of experiments.