Thermodynamics of Energy Magnetization

TL;DR

This paper develops a thermodynamic framework for energy magnetization under gravitomagnetic fields, deriving explicit formulas and validating them through a Chern insulator example.

Contribution

It introduces a modified free energy approach to account for energy current changes and rigorously establishes the Streda formula for thermal Hall conductivity.

Findings

Derived explicit expression for energy magnetization in periodic systems

Established the Streda formula for thermal Hall conductivity

Validated theory with a Chern insulator example

Abstract

We construct the thermodynamics of energy magnetization in the presence of gravitomagnetic field. We show that the free energy must be modified to account for the modification of the energy current operator in the presence of a confining potential. The explicit expression of the energy magnetization is derived for a periodic system, and the Streda formula for the thermal Hall conductivity is rigorously established. We demonstrate our theory of the energy magnetization and the Streda formula in a Chern insulator.