Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems

TL;DR

This paper develops thermodynamic formulas for persistent currents and magnetization in 2D magnetic quantum systems, analyzing their behavior under various magnetic field configurations and symmetries.

Contribution

It introduces general thermodynamic relations for these phenomena and demonstrates their validity in systems with translation and rotation invariance, including specific physical models.

Findings

Classical relationship between current and magnetization holds under symmetry conditions.

Derived formulas apply to systems with point vortices and homogeneous magnetic fields.

Analyzed effects of random magnetic impurities on persistent currents.

Abstract

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the ``classical'' relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed to an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).