Orbital magnetization from parallel transport of Bloch states
Abstract
Quantum geometric formulations of linear and nonlinear responses can be constructed from a single building block in the form of a gauge-invariant interband transition operator. Here, we identify a second building block for quantum geometry: a band-resolved adiabatic connection operator that captures the noncommutativity between band projectors and their momentum derivatives. The band-resolved adiabatic connection operator, first introduced in the theory of adiabatic driving, serves as a generalized angular momentum within the state manifold of single bands, and we employ it to reformulate expressions for the band-resolved orbital magnetic moment. This form provides a complementary geometric interpretation alongside the multiband separation between energetic- and quantum-state properties by the two-state Berry curvature. Our formalism allows us to present formulas valid for both nondegenerate and degenerate bands, thereby removing the limitations of the common Bloch-state formula. We illustrate our theory by calculating a large orbital magnetization emerging without spin-orbit coupling in a spin-compensated, noncoplanar anomalous Hall magnet with degenerate bands.
Keywords
Cite
@article{arxiv.2512.09051,
title = {Orbital magnetization from parallel transport of Bloch states},
author = {Johannes Mitscherling and Jan Priessnitz and Libor Šmejkal},
journal= {arXiv preprint arXiv:2512.09051},
year = {2025}
}