Hall conductivity beyond the linear response regime

TL;DR

This paper presents a semi-analytical approach to calculate Hall conductivity beyond linear response, revealing how strong electric fields affect Hall current in systems like cold Bose atoms in optical lattices.

Contribution

It introduces a novel semi-analytical method that extends Hall conductivity calculations beyond linear response theory for single-band systems.

Findings

Hall current decreases with increasing electric field when Bloch frequency exceeds cyclotron frequency.

Method applicable to cold Bose atoms in 2D optical lattices.

No limitations on electric field magnitude in the new approach.

Abstract

The paper introduces a semi-analytical method for calculating the Hall conductivity in the single-band approximations. The method goes beyond the linear response theory and, thus, imposes no limitation on the electric fields magnitude. It is shown that the Hall current decreases with increase of the electric field, if the Bloch frequency (which is proportional to the electric field) exceeds the cyclotron frequency (which is proportional to the magnetic field). The obtained results can be directly applied to the system of cold Bose atoms in a 2D optical lattice, where the single-band approximation is well justified.