Molecular Berry curvatures and the adiabatic response tensors

TL;DR

This paper demonstrates that three well-known adiabatic response tensors can be derived directly from the general Berry curvature framework, confirming their formulas as specific cases without requiring separate proofs.

Contribution

It shows that the formulas for the atomic polar tensor, atomic axial tensor, and rotational g factor are direct applications of the general Berry curvature expression, unifying their derivations.

Findings

Confirmed the known formulas as special cases of the general Berry curvature expression.

Unified the derivation of three adiabatic response tensors under a common framework.

Provided a general perspective on adiabatic response tensors in many-electron systems.

Abstract

Adiabatic transport in a many-electron system is expressed in terms of the appropriate Berry curvature, owing to the Niu-Thouless theory [J. Phys A {\bf 17}, 2453 (1984)]; the main equation is very compact and very general. I address here three paradigmatic adiabatic response tensors -- -the atomic polar tensor, the atomic axial tensor, and the rotational $g$ factor -- and I show that, for all of them, the known formulas do not need an independent proof. They are just case studies of the general expression, for different choices the curvature's two arguments.