Collective Excitations of Dirac Electrons in Graphene

TL;DR

This paper explores the collective excitations of Dirac electrons in graphene, revealing unique stability of fractional quantum Hall states and the existence of undamped plasmon modes influenced by magnetic fields and spin-orbit interaction.

Contribution

It provides new insights into the behavior of collective excitations in graphene, especially regarding fractional quantum Hall states and plasmon modes under various conditions.

Findings

Fractional quantum Hall state most stable at ν=1/m in the n=1 Landau level.

Existence of undamped plasmon mode in the gap of the single-particle continuum with spin-orbit interaction.

Distinct behavior of collective excitations compared to conventional 2D electron systems.

Abstract

Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence of an external magnetic field. Unlike in the conventional two-dimensional electron system, the $\nu=\frac1m$ fractional quantum Hall state in graphene was found to be most stable in the $n=1$ Landau level. In the zero field case, but in the presence of the spin-orbit interaction, an undamped plasmon mode was found to exist in the gap of the single-particle continuum.