Dynamical polarization, screening, and plasmons in gapped graphene

TL;DR

This paper calculates the polarization function of gapped graphene at zero temperature, revealing how a band gap influences plasmon dispersion and screening, including the emergence of a new undamped plasmon mode.

Contribution

It provides an analytical expression for the polarization function of gapped graphene and explores its effects on plasmon modes and screening properties.

Findings

A new undamped plasmon mode appears with a small band gap.

The plasmon dispersion follows the usual square root behavior at long wavelengths.

Screening shows slower decay of Friedel oscillations ($1/r^2$) compared to gapless graphene.

Abstract

The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap. The result is expressed in terms of elementary functions and is used to find the dispersion of the plasmon mode and the static screening within the random phase approximation. At long wavelengths the usual square root behaviour of plasmon spectra for two-dimensional (2D) systems is obtained. The presence of a small (compared to a chemical potential) gap leads to the appearance of a new undamped plasmon mode. At greater values of the gap this mode merges with the long-wavelength one, and vanishes when the Fermi level enters the gap. The screening of charged impurities at large distances differs from that in gapless graphene by slower decay of Friedel oscillations ($1/r^2$ instead of $1/r^3$), similarly to conventional 2D systems.