Unusual Microwave Response of Dirac Quasiparticles in Graphene

Abstract

Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small the intraband response can exhibit a cusp around zero frequency $Ω$ and this unusual lineshape changes to Drude-like by increasing the chemical potential $|μ|$, with width also increasing linearly with $μ$. The interband contribution at T=0 is a constant independent of $Ω$ with a lower cutoff at $2 μ$. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap $Δ$. At large magnetic field $B$, the diagonal and Hall conductivities at small $Ω$ become independent of $B$ but remain nonzero and show structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, $E_0 = \pm Δ$, is field independent in sharp contrast to the conventional case.