Conductivity in quasi two-dimensional systems

TL;DR

This paper develops a quantum kinetic approach to calculate conductivity in quasi two-dimensional systems, incorporating advanced diagrammatic corrections and analyzing weak localization effects, with applications to impurity interactions and metal-insulator transitions.

Contribution

It introduces a method extending the GW approximation to include maximally crossed diagrams and field-dependent collision integrals for conductivity calculations.

Findings

Weak localization correction arises from field dependence of collision integral.

Dynamical screening causes linear temperature dependence in conductivity.

Neutral impurities lead to Fermi-liquid behavior in low-temperature conductivity.

Abstract

The conductivity in quasi two-dimensional systems is calculated using the quantum kinetic equation. Linearizing the Lenard-Balescu collision integral with the extension to include external field dependences allows one to calculate the conductivity with diagrams beyond the GW approximation including maximally crossed lines. Consequently the weak localization correction as an interference effect appears here from the field dependence of the collision integral (the latter dependence sometimes called intra-collisional field effect). It is shown that this weak localization correction has the same origin as the Debye-Onsager relaxation effect in plasma physics. The approximation is applied to a system of quasi two-dimensional electrons in hetero-junctions which interact with charged and neutral impurities and the low temperature correction to the conductivity is calculated analytically. It turns out that the dynamical screening due to charged impurities leads to a linear temperature dependence, while the scattering from neutral impurities leads to the usual Fermi-liquid behavior. By considering an appropriate mass action law to determine the ratio of charged to neutral impurities we can describe the experimental metal-insulator transition at low temperatures as a Mott-Hubbard transition.