Nonlinear Steady-State Mesoscopic Transport, I. Formalism

TL;DR

This paper introduces a maximum entropy-based formalism for nonlinear steady-state mesoscopic transport, successfully explaining high-current phenomena like the integer quantum Hall effect by considering state occupancy dependence on current and energy.

Contribution

It develops a new formalism for nonlinear mesoscopic transport that accounts for current-dependent state occupancy, improving upon traditional reservoir models.

Findings

Successfully explains quantization in high-current regimes

Highlights limitations of reservoir models outside linear response

Provides a framework for high-precision Hall measurements

Abstract

We present an approach to steady-state mesoscopic transport based on the maximum entropy principle formulation of nonequilibrium statistical mechanics. This approach is valid in the nonlinear regime of high current, and yields the quantization observed in the integer quantum Hall effect at large currents. A key ingredient of this approach, and its success in explaining high-precision Hall measurements, is that the occupancy of single-electron states depends on their current as well as their energy. This suggests that the reservoir picture commonly used in mesoscopic transport is unsatisfactory outside of linear response.