Statistical model for the effects of phase and momentum randomization on electron transport

TL;DR

This paper introduces a statistical model that independently adjusts phase and momentum randomization to study their effects on electron transport, bridging quantum and classical regimes efficiently.

Contribution

It presents a novel model based on Büttiker's approach that allows independent control of phase and momentum dephasing, providing new insights into transport properties.

Findings

Dephasing-driven transition from localization to ohmic behavior is unaffected by momentum randomization.

The model reduces computation time compared to previous approaches.

Derived an efficient formula for disorder-averaged resistance in tight-binding chains.

Abstract

A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to describe the transport in an intermediate regime between classic and quantum transport. The model is based on B\"uttiker's approach using fictitious reservoirs for the dephasing effects. However, in contrast to other models, at the fictitious reservoirs complete phase randomization is assumed, which effectively divides the system into smaller coherent subsystems, and an ensemble average over randomly distributed dephasing reservoirs is calculated. This approach reduces not only the computation time but allows also to gain new insight into system properties. In this way, after deriving an efficient formula for the disorder-averaged resistance of a tight-binding chain, it is shown that the dephasing-driven transition from localized-exponentially to ohmic-linear behavior is not affected by the degree of momentum randomizing dephasing.