Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures

TL;DR

This paper studies quantum corrections to conductivity in weakly disordered conductors, highlighting how electron-electron and electron-phonon interactions influence temperature-dependent conductivity across different dimensional regimes.

Contribution

It provides a detailed analysis of quantum interference effects on conductivity, including new temperature dependencies in quasi-1D, 2D, and 3D conductors, considering electron-electron and electron-phonon interactions.

Findings

Electron-electron interaction causes a negative $T^2 \, \ln T$ correction in 3D.

In quasi-2D conductors, the correction is linear in temperature.

In quasi-1D conductors, the correction scales as $T^2$.

Abstract

We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimensional conductor, temperature-dependent correction is proportional to $T^2$. The electron interaction via exchange of virtual phonons also gives $T^2$-correction. The contribution of thermal phonons interacting with electrons via the screened deformation potential results in $T^4$-term and via unscreened deformation potential results in $T^2$-term. The interference contributions dominate over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.