A comparative study of some models of incoherence at the mesoscopic scale

TL;DR

This paper compares two phenomenological models of incoherent electron transport at the mesoscopic scale, highlighting their physical differences and validating them against experimental phenomena such as tunneling, magneto-conductance, and Fano resonances.

Contribution

It introduces and compares the Coherent Absorption and Wave Attenuation models, identifying physical issues in the former and validating the latter with experimental data.

Findings

Wave Attenuation model aligns better with experimental results.

Coherent Absorption model exhibits physical inconsistencies.

Both models explain phenomena like resonant tunneling and Aharonov-Bohm oscillations.

Abstract

The pre-existing literature on phenomena at the mesoscopic scale is concerned among other things with phase coherent transport. Phase coherent transport dominates at very low temperatures. With increase in temperature, as the system size becomes comparable to the inelastic mean free path phase incoherence sets in. This incoherence further leads to dephasing, and as a consequence purely quantum effects in electron transport give way to classical macroscopic behavior. In this work we consider two distinct phenomenological models of incoherent transport, the Coherent Absorption and Wave Attenuation models. We reveal some physical problems in the Coherent Absorption model as opposed to the Wave Attenuation model. We also compare our proposed model with experiments in case of the much studied peak to valley ratios in resonant tunneling diodes, magneto-conductance oscillations and Fano resonances in case of Aharonov-Bohm rings.