Non-Hermitian magnetic moment

TL;DR

This paper develops a semiclassical framework for non-Hermitian periodic systems, deriving magnetic properties and generalizing angular momentum to account for non-Hermitian effects.

Contribution

It introduces a non-Hermitian semiclassical theory, defining a meaningful angular momentum and magnetic moment in such systems, including their imaginary components.

Findings

Derived the energy of wavepackets in non-Hermitian systems with perturbations.

Established a non-Hermitian angular momentum compatible with the real part of magnetic moments.

Discussed the origin of the imaginary magnetic moment component from a non-Hermitian Aharonov-Bohm effect.

Abstract

We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wavepacket to first order in the gradients of the perturbations. Applying the theory to the specific case of a uniform external magnetic field, we obtain an expression for the orbital magnetization energy. Using the principles of non-Hermitian dynamics, we define a physically meaningful non-Hermitian generalization of the angular momentum operator and show that it is compatible with the real part of the orbital magnetic moment. The imaginary part of the orbital magnetic moment is also discussed and shown to originate from an imaginary counterpart to the angular momentum that gives rise to a non-Hermitian generalization of the Aharonov-Bohm effect.