Finite-temperature Screening and the Specific Heat of Doped Graphene Sheets

TL;DR

This paper derives a semi-analytical finite-temperature response function for doped graphene's electrons, enabling precise predictions of its specific heat and compressibility, and confirming Fermi-liquid behavior at low temperatures.

Contribution

It provides the first semi-analytical finite-temperature response function for doped graphene, facilitating accurate thermodynamic property calculations.

Findings

Specific heat exhibits linear temperature dependence at low temperatures.

Renormalized quasiparticle velocity controls the specific heat slope.

Results confirm Fermi-liquid behavior in doped graphene.

Abstract

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting massless Dirac fermions (the so-called "Lindhard" function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the Random Phase Approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.