Interband effect to nonlinear charge response in semiconductor nanostructures

Determining spin-orbit interaction (SOI) is an important task for the investigation of semiconductor nanostructures aiming at the usage of quantum computing. While it is known that nonlinear conductivity is sensitive to the strength and type of SOI, many calculations of nonlinear transport coefficients rely on Boltzmann transport theory, which uses simplistic assumptions about further quantum effects.

We develop and utilize a microscopic theory based on the Keldysh formalism which naturally accounts for interband transitions such as Berry curvature and enables a more accurate treatment of impurity scattering. We examine the second-order charge response to the electric field of effective two-band models in one-dimensional nanowires and two-dimensional hole gases. We find that in nanostructures, due to their small energy scales, interband contributions can be significant, especially when the relaxation time is comparatively small, potentially altering the qualitative features found using purely semiclassical approaches. Nonetheless, we discover that different types of SOI (linear or cubic) result in drastically different in-plane magnetic field angle dependencies, even when interband effects are relevant. Our results provide a detailed understanding of when interband effects become important in nonlinear transport and lay the groundwork for predicting other nonlinear transport effects in various materials and devices.