Coulomb interaction in graphene: Relaxation rates and transport

TL;DR

This paper investigates how finite temperature and electron-electron interactions influence inelastic scattering, relaxation, and transport in clean graphene, revealing non-monotonic energy dependence and plasmon effects on conductivity.

Contribution

It provides a detailed analysis of inelastic scattering rates and transport properties in graphene considering finite temperature effects, plasmon resonances, and interaction screening.

Findings

Finite temperature significantly alters screening and scattering rates.

Identifies a hierarchy of regimes due to plasmon enhancement and screening.

Reveals non-monotonic energy dependence of relaxation rates in graphene.

Abstract

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic scattering rates as compared to the zero-temperature case. Focussing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing of interference processes. We identify an hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a non-monotonic energy dependence of the inelastic relaxation rates in clean graphene which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic-equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly non-equilibrium setups.