Density dependent exchange contribution to $\partial\mu/\partial n$ in extrinsic graphene

TL;DR

This paper calculates how the chemical potential's derivative with respect to carrier density in extrinsic graphene varies with density, revealing a weak exchange effect and a specific density dependence, using Hartree-Fock approximation.

Contribution

It provides the first detailed calculation of $rac{ ext{d}\mu}{ ext{d}n}$ in extrinsic graphene considering exchange interactions, highlighting differences from intrinsic graphene.

Findings

$rac{ ext{d}\mu}{ ext{d}n}$ scales as $n^{-rac{1}{2}}$ with density.

Exchange effects cause about 20% enhancement over the bare value.

The Dirac-point singularity present in intrinsic graphene is absent in extrinsic graphene.

Abstract

We calculate $\partial\mu/\partial n$ in extrinsic graphene as a function of carrier density $n$ at zero temperature by obtaining the electronic self-energy within the Hartree-Fock approximation. The exchange-driven Dirac-point logarithmic singularity in the quasiparticle velocity of intrinsic graphene disappears in the extrinsic case. The calculated renormalized $\partial\mu/\partial n$ in extrinsic graphene has the same qualitative $n^{-\frac12}$ density dependence as the inverse bare density of states with a 20% enhancement from the corresponding bare value, a relatively weak effect compared to the corresponding parabolic-band case.