Orbital Magnetism in Ensembles of Ballistic Billiards

TL;DR

This paper investigates the magnetic response of small 2D structures using semiclassical methods, revealing that short classical trajectories dominate the susceptibility, which is notably enhanced in regular systems like squares, aligning with experimental observations.

Contribution

It introduces a semiclassical approach focusing on short trajectories to analyze orbital magnetism in ballistic billiards, providing new insights into susceptibility enhancements.

Findings

Short classical trajectories dominate magnetic response.

Regular systems exhibit enhanced susceptibility.

Results agree with recent experimental measurements.

Abstract

We calculate the magnetic response of ensembles of small two-dimensional structures at finite temperatures. Using semiclassical methods and numerical calculation we demonstrate that only short classical trajectories are relevant. The magnetic susceptibility is enhanced in regular systems, where these trajectories appear in families. For ensembles of squares we obtain a large paramagnetic susceptibility, in good agreement with recent measurements in the ballistic regime.