Current response of nonequilibrium steady states in Landau-Zener problem: Nonequilibrium Green's function approach

TL;DR

This paper develops a Green's function framework to analyze the current response of insulators under strong electric fields, revealing complex behaviors beyond simple tunneling models and predicting nonreciprocal transport phenomena.

Contribution

It introduces a semi-quantitative Green's function approach for nonequilibrium steady states in insulators with electric fields, including nonperturbative effects and nonreciprocal transport predictions.

Findings

Current response is more complex than intraband tunneling models suggest.

Derived a semi-quantitative formula for nonequilibrium Green's functions.

Predicted nonreciprocal charge and spin transport in noncentrosymmetric insulators.

Abstract

The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic reservoir. Using asymptotic expansion techniques, we derive a semi-quantitative formula for the Green's function with nonperturbative contribution. This formalism enables us to calculate dissipative current response of the nonequilibrium steady state, which turns out to be not simply characterized by the intraband current proportional to the tunneling probability. We also apply the present formalism to noncentrosymmetric insulators, and propose nonreciprocal charge and spin transport peculiar to tunneling electrons.