Wigner-function formalism applied to semiconductor quantum devices: Need for nonlocal scattering models

TL;DR

This paper highlights the limitations of local scattering models in Wigner-function formalism for quantum devices and introduces nonlocal models to improve physical accuracy.

Contribution

It demonstrates the unphysical results of local models and proposes a quantum-mechanical generalization with nonlocal scattering superoperators.

Findings

Local models cause unphysical suppression of relaxation.

Nonlocal models restore correct thermalization dynamics.

Positivity of probability density is maintained with nonlocal models.

Abstract

In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we show that the use of such local scattering approaches within the Wigner-function formalism may lead to unphysical results, namely anomalous suppression of intersubband relaxation, incorrect thermalization dynamics, and violation of probability-density positivity. Furthermore, we propose a quantum-mechanical generalization of relaxation-time and Boltzmann-like models, resulting in nonlocal scattering superoperators that enable one to overcome such limitations.