Electromagnetic response and effective gauge theory of graphene in a magnetic field

TL;DR

This paper investigates graphene's electromagnetic response in a magnetic field, highlighting its unique dielectric properties, screening effects, and deriving an effective gauge theory that links susceptibilities to Hall conductance.

Contribution

It introduces a novel effective gauge theory for graphene's response, emphasizing its dielectric behavior and screening effects in a magnetic field.

Findings

Graphene's vacuum acts as a dielectric medium with significant susceptibilities.

Coulomb interactions are efficiently screened, reducing exciton spectra.

Electric susceptibility relates to Hall conductance and Landau gap.

Abstract

The electromagnetic response of graphene in a magnetic field is studied, with particular emphasis on the quantum features of its ground state (vacuum). The graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric medium and carries an appreciable amount of electric and magnetic susceptibilities. The dielectric effect grows rapidly with increasing filling factor nu in such a way that reflects the 'relativistic' Landau-level characteristics of graphene as well as its valley and spin degeneracy. A close look into the dielectric function also reveals that the Coulomb interaction is efficiently screened on the scale of the magnetic length, leading to a prominent reduction of the exciton spectra in graphene. In addition, an effective gauge theory of graphene is constructed out of the response. It is pointed out thereby that the electric susceptibility is generally expressed as a ratio of the Hall conductance to the Landau gap.