Interband contributions to nonlinear transport in semiconductor nanostructures

TL;DR

This paper develops a microscopic Keldysh formalism to analyze nonlinear transport in semiconductor nanostructures, highlighting the importance of interband effects and Berry curvature, especially in disordered systems, and distinguishes the impact of different spin-orbit interactions.

Contribution

It introduces a microscopic approach beyond semiclassical theory to account for interband transitions and impurity effects in nonlinear transport in nanostructures.

Findings

Interband contributions are significant in nanostructures, especially in the dirty limit.

Different types of spin-orbit interaction produce distinct in-plane field angle dependences.

Interband effects can modify qualitative features predicted by semiclassical models.

Abstract

Spin-orbit interaction (SOI) is a crucial ingredient for many potential applications of quantum devices, such as the use of semiconductor nanostructures for quantum computing. It is known that nonlinear conductivities are sensitive to the strength and type of SOI, however, many calculations of nonlinear transport coefficients are based on the semiclassical Boltzmann theory and make simplifying assumptions about scattering effects due to disorder. In this paper we develop and employ a microscopic theory based on the Keldysh formalism that goes beyond simple semiclassical approximations. This approach, for instance, naturally takes into account the effects of interband transitions, Berry curvature, and allows for a more precise treatment of impurity scattering. As a test of this formalism, we consider the nonlinear transport properties in an effective two-band model of one-dimensional nanowires (1DNWs) and two-dimensional hole gases (2DHGs) in the presence of a magnetic field causing Zeeman splittings of the spin states. We find that the small energy scales in nanostructures mean that interband contributions can be relevant, especially in the dirty limit, and therefore could modify qualitative features found using a purely semiclassical approach. Nonetheless, we find that different types of SOI (linear or cubic) still result in remarkably pronounced different in-plane field angle dependences, which survive even when interband effects are relevant. Our results provide a detailed understanding of when interband effects become important for nonlinear transport and can serve as the basis for a microscopic description to predict other nonlinear transport effects in materials and devices.