# Geometric orbital magnetization in adiabatic processes

## TL;DR

This paper introduces a geometric contribution to orbital magnetization in adiabatic processes of gapped electrons, linking it to the many-body Berry phase and topological invariants.

## Contribution

It identifies and formulates the geometric orbital magnetization as a derivative of the many-body Berry phase, including topological and non-topological components.

## Key findings

- The geometric orbital magnetization arises from adiabatic time evolution.
- It decomposes into topological and non-topological parts in 2D insulators.
- The topological part is expressed as a third Chern-Simons form.

## Abstract

We consider periodic adiabatic processes of gapped many-body spinless electrons. We find an additional contribution to the orbital magnetization due to the adiabatic time evolution, dubbed \textit{geometric} orbital magnetization, which can be expressed as derivative of the many-body Berry phase with respect to an external magnetic field. For two-dimensional band insulators, we show that the geometric orbital magnetization generally consists of two pieces, the topological piece that is expressed as third Chern-Simons form in $(t,k_x,k_y)$ space, and the non-topological piece that depends on Bloch states and energies of both occupied and unoccupied bands.