Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons

TL;DR

This study investigates how impurity scattering, Coulomb interactions, and optical phonons influence the electrical and thermal transport properties of graphene, providing a comprehensive model that aligns with experimental observations.

Contribution

It offers a combined analysis of multiple scattering mechanisms affecting graphene's transport properties, including an analytical solution for impurity scattering and numerical solutions for combined effects.

Findings

Screened Coulomb impurity scattering violates Wiedemann-Franz law at low temperatures.

Crossover from hydrodynamic to Fermi-liquid regime observed with varying scattering.

Optical phonons significantly affect thermopower at relatively low temperatures.

Abstract

We study the electric and thermal transport of the Dirac carriers in monolayer graphene using the Boltzmann-equation approach. Motivated by recent thermopower measurements [F. Ghahari, H.-Y.~Xie, T. Taniguchi, K. Watanabe, M.~S.~Foster, and P.~Kim, Phys.\ Rev.\ Lett.\ {\bf 116}, 136802 (2016)], we consider the effects of quenched disorder, Coulomb interactions, and electron--optical-phonon scattering. Via an unbiased numerical solution to the Boltzmann equation we calculate the electrical conductivity, thermopower, and electronic component of the thermal conductivity, and discuss the validity of Mott's formula and of the Wiedemann-Franz law. An analytical solution for the disorder-only case shows that screened Coulomb impurity scattering, although elastic, violates the Wiedemann-Franz law even at low temperature. For the combination of carrier-carrier Coulomb and short-ranged impurity scattering, we observe the crossover from the interaction-limited (hydrodynamic) regime to the disorder-limited (Fermi-liquid) regime. In the former, the thermopower and the thermal conductivity follow the results anticipated by the relativistic hydrodynamic theory. On the other hand, we find that optical phonons become nonnegligible at relatively low temperatures and that the induced electron thermopower violates Mott's formula. Combining all of these scattering mechanisms, we obtain the thermopower that quantitatively coincides with the experimental data.