Polarization Charge Distribution in Gapped Graphene

TL;DR

This paper analyzes how vacuum polarization charge from a Coulomb impurity is distributed in gapped graphene, revealing a complex spatial pattern influenced by the effective Compton wavelength, with results supported by both analytical and numerical methods.

Contribution

It provides an analytical and numerical study of the polarization charge distribution in gapped graphene, including effects of electron-electron interactions, which was not previously detailed.

Findings

Charge density exhibits a non-trivial spatial distribution.

Transition from logarithmic to power-law behavior at the characteristic length scale.

Continuum results are validated by lattice model diagonalization.

Abstract

We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.