Magnetization of Disordered Ballistic Quantum Billards

TL;DR

This paper investigates the magnetic response of mesoscopic ballistic quantum dots with disorder, revealing disorder-independent paramagnetic susceptibility and disorder-dependent flux susceptibility, aligning with experimental observations.

Contribution

It introduces a semiclassical approach to analyze how static disorder influences magnetic properties in ballistic quantum dots, highlighting new disorder effects.

Findings

Disorder induces a large linear paramagnetic susceptibility in magnetic fields.

Susceptibility depends on disorder and is proportional to the mean free path in flux scenarios.

Results agree with recent experimental measurements.

Abstract

We study the magnetic response of mesoscopic quantum dots in the ballistic regime where the mean free path $l_e$ is larger that the size $L$ of the sample, yet smaller than $L (k_F L)^{d-1}$. In this regime, disorder plays an important role. Employing a semiclassical picture we calculate the contribution of long trajectories which are strongly affected by static disorder and which differ sharply from those of clean systems. In the case of a magnetic field, they give rise to a large linear paramagnetic susceptibility (which is disorder independent), whose magnitude is in agreement with recent experimental results. In the case of a Aharonov-Bohm flux, the susceptibility is disorder dependent and is proportional to the mean free path as in the diffusive regime. We also discuss the corresponding non--linear susceptibilities.