Dynamical polarization of monolayer graphene in a magnetic field

TL;DR

This paper provides an exact analytical calculation of the dynamical polarization function of monolayer graphene in a magnetic field, revealing oscillatory screening behavior influenced by magnetic field and chemical potential.

Contribution

It derives a comprehensive analytic expression for graphene's polarization function in magnetic fields, incorporating effects of finite chemical potential, temperature, and Landau level broadening.

Findings

Polarization function expressed in terms of digamma functions and Laguerre polynomials.

Screening length oscillates with magnetic field and chemical potential.

Inverse screening length vanishes when Fermi level is between Landau levels.

Abstract

The one-loop dynamical polarization function of graphene in an external magnetic field is calculated as a function of wavevector and frequency at finite chemical potential, temperature, band gap, and width of Landau levels. The exact analytic result is given in terms of digamma functions and generalized Laguerre polynomials, and has the form of double sum over Landau levels. Various limits (static, clean, etc) are discussed. The Thomas-Fermi inverse length $q_F$ of screening of the Coulomb potential is found to be an oscillating function of a magnetic field and a chemical potential. At zero temperature and scattering rate, it vanishes when the Fermi level lies between the Landau levels.