Hall conductivity beyond the linear response regime

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.

13 pages, 4 figures

References in corpus (4)

• Synthetic magnetic fields for ultracold neutral atoms
• Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
• Cyclotron-Bloch dynamics of a quantum particle in a 2D lattice
• Quantum Hall effect beyond the linear response approximation

Cited by in corpus (4)

• Quantum response theory for open systems and its application to Hall conductance
• The driven Harper model
• Master equation approach to conductivity of bosonic and fermionic carriers in one- and two-dimensional lattices
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics