Master equation approach to conductivity of bosonic and fermionic carriers in one- and two-dimensional lattices

TL;DR

This paper presents a master equation approach to analyze the conductivity of bosonic and fermionic carriers in 1D and 2D lattices, capturing linear and nonlinear responses, including Hall effect inversion.

Contribution

It introduces a master equation framework that reproduces known linear response results and extends to nonlinear regimes, revealing new effects like Hall current inversion.

Findings

Reproduces all known linear response results, including quantum Hall effect.

Allows calculation of nonlinear current responses beyond linear regime.

Shows Hall current can be inverted by changing electric field orientation.

Abstract

We discuss the master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, we show that the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.