Degeneracy-projected polarization formulas for Hall-type conductivities

TL;DR

This paper introduces simplified, computationally efficient formulas for Hall-type conductivities using degeneracy-projected polarizations, applicable to general Hamiltonians without gap restrictions, and explores their physical implications.

Contribution

It presents new on-shell commutator formulas for Hall conductivities that are easier to compute and apply broadly, including in disordered systems and open boundary conditions.

Findings

Hall currents in open boundaries are carried by gapless chiral excitations

Formulas are applicable to general Hamiltonians without a gap restriction

Finite lattice calculations can be extrapolated to the DC limit in disordered metals

Abstract

Kubo formulas for Hall, transverse thermoelectric and thermal Hall conductivities are simplified into on-shell commutators of degeneracy projected polarizations. The new expressions are computationally economical, and apply to general Hamiltonians without a gap restriction. We show that Hall currents in open boundaries are carried by gapless chiral excitations. Extrapolation of finite lattice calculations to the DC-thermodynamic limit is demonstrated for a disordered metal.