Orbital Magnetism in Two-dimensional Integrable Systems

TL;DR

This paper investigates the orbital magnetism of a degenerate electron gas in various two-dimensional integrable systems using linear response theory, highlighting different temperature regimes and finite-size effects.

Contribution

It provides a detailed analysis of magnetic susceptibility across multiple temperature regimes in 2D integrable systems, including analytic expressions for specific cases.

Findings

Finite-size effects significantly influence susceptibility in microscopic and mesoscopic regimes.

Susceptibility approaches macroscopic values at high temperatures.

Analytic expressions for susceptibility are derived for certain systems.

Abstract

We study orbital magnetism of a degenerate electron gas in a number of two-dimensional integrable systems, within linear response theory. There are three relevant energy scales: typical level spacing, the energy related to the inverse time of flight across the system, and the Fermi energy. Correspondingly, there are three distinct temperature regimes: microscopic, mesoscopic, and macroscopic. In the first two regimes there are large finite-size effects in the magnetic susceptibility, whereas in the third regime the susceptibility approaches its macroscopic value. In some cases, such as a quasi-one-dimensional strip or a harmonic confining potential, it is possible to obtain analytic expressions for the susceptibility in the entire temperature range.