Resistivity of non-Galilean invariant two dimensional Dirac system

TL;DR

This paper investigates how electron-electron interactions influence resistivity in two-dimensional Dirac systems, revealing a T^2 temperature dependence experimentally confirmed in HgTe quantum wells, challenging previous assumptions.

Contribution

It demonstrates that electron-electron scattering can significantly affect conductivity in Dirac systems, producing observable T^2 resistivity corrections, contrary to conventional systems.

Findings

T^2 resistivity correction confirmed experimentally in HgTe quantum wells

T^4 behavior predicted but not observed due to localization effects

Electron-electron scattering impacts conductivity in Dirac materials

Abstract

We revisited the influence of electron-electron scattering on the resistivity of a two-dimensional system with linear spectrum. In conventional systems with parabolic spectrum, where Umklapp scattering is either prohibited or ineffective due to small Fermi surface, particle-particle scattering does not contribute to conductivity because it does not change the total momentum. However, within the framework of Boltzmann kinetic model, we demonstrate that electron-electron scattering in Dirac systems can significantly contribute to conductivity, producing distinct temperature-dependent corrections: a T\textsuperscript{4} behavior at low temperatures and T\textsuperscript{2} dependence at moderate temperatures. While the predicted T\textsuperscript{4} scaling is not observed experimentally -- likely suppressed by dominant weak localization effects -- the T\textsuperscript{2} scaling is clearly confirmed in our measurements. Specifically, temperature-dependent resistivity data from gapless single-valley HgTe quantum well exhibit T\textsuperscript{2} corrections, which align well with theoretical predictions. Thus, we challenge the paradigm that T\textsuperscript{2} term in resistivity is absent in single-band 2D metals.