Electron-Electron Scattering and Resistivity in Non-Centrosymmetric Metals

TL;DR

This paper investigates how electron-electron scattering influences low-temperature resistivity in non-centrosymmetric metals with spin-orbit coupling, showing the quadratic temperature dependence persists under certain conditions.

Contribution

It derives the temperature dependence of electron-electron collision rates in non-centrosymmetric metals considering spin-orbit effects and impurity scattering, extending understanding of resistivity behavior.

Findings

Quadratic low-temperature resistivity remains valid with significant spin-orbit splitting.

Electron-electron scattering rate depends on band splitting and impurity scattering.

Resistivity behavior is similar to centrosymmetric metals under specific conditions.

Abstract

The quadratic low-temperature dependence of resistance in ordinary metals is determined by the momentum relaxation due to electron-electron scattering in the presence Umklapp processes and scattering on impurities. In metals without inversion center spin-orbit interaction of electrons with crystal lattice lifts spin degeneracy of electron states and splits each band on two bands. The temperature dependence of electron-electron collisions scattering rate is found using the matrix kinetic equation including the electron-impurity and electron-electron intra and inter band scattering. It is shown that in clean enough case when the energy of band splitting exceeds the electron-impurity scattering rate but at the same time it is much smaller than the Fermi energy the square low-temperature dependence of resistivity is still valid.