Orbital magnetism of coupled bands models

TL;DR

This paper develops a gauge-independent perturbation theory for orbital magnetism in 2D tight-binding models, revealing new formulas for susceptibility and uncovering surprising magnetic behaviors due to interband effects.

Contribution

It introduces a gauge-independent perturbation framework and derives a new general formula for orbital susceptibility in coupled-band models.

Findings

Derived a new formula for orbital susceptibility including interband effects.

Identified phenomena like in-gap diamagnetism and band edge paramagnetism.

Applied theory to various two-band systems, revealing unexpected magnetic features.

Abstract

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called {\it modern theory of orbital magnetization} and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band -- either gapless or gapped -- systems. We point out some surprising features in the orbital susceptibility -- such as in-gap diamagnetism or parabolic band edge paramagnetism -- coming from interband coupling. From that we draw general conclusions on the orbital magnetism of itinerant electrons in multi-band tight-binding models.