Topological Features of the Magnetic Response in Inhomogeneous Magnetic Fields

TL;DR

This paper explores the topological characteristics of magnetic responses in a 2D electron gas subjected to inhomogeneous magnetic fields, emphasizing non-perturbative effects and the Aharonov-Bohm flux line.

Contribution

It introduces a topological analysis of magnetic responses in 2D electron gases, extending the understanding of non-perturbative effects in inhomogeneous magnetic fields.

Findings

Topological features of magnetic responses are characterized using Index theory.

The Aharonov-Bohm flux line case is analyzed in detail.

Results are generalized to broader inhomogeneous magnetic field scenarios.

Abstract

We present topological features of the magnetic response (orbital and spin) of a two-dimensional degenerate and non interacting electron gas due to inhomogeneous applied magnetic fields. These issues are analysed from the point of view of the Index theory with a special emphasis on the non perturbative aspects of this response. The limiting case of a Aharonov-Bohm magnetic flux line is studied in details and the results are extended to more general situations.