h/2e oscillations and quantum chaos in ballistic Aharonov-Bohm billiards

TL;DR

This paper investigates quantum interference effects in ballistic Aharonov-Bohm billiards under weak magnetic fields, revealing h/2e oscillations, their damping, and the influence of classical chaos on quantum phenomena.

Contribution

It introduces a semi-classical scattering approach to analyze h/2e oscillations and magnetoresistance in chaotic and regular billiard systems.

Findings

h/2e oscillations caused by time-reversed trajectories

Negative magnetoresistance observed with magnetic field

Dampening of oscillations linked to classical dynamics

Abstract

We study the quantum interference effect for the single ballistic Aharonov-Bohm billiard in the presence of a weak magnetic field B. The diagonal part of the wave-number averaged reflection coefficient $\delta {\cal R}_D$ is calculated by use of semi-classical scattering theory. In addition to the appearance of "h/2e oscillation" that are caused by interference between time-reversed coherent backscattering classical trajectories, B in the conducting region leads to negative magnetoresistance and dampening of the h/2e oscillation amplitude. The B dependence of the results reflects the underlying classical (chaotic and regular) dynamics.