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 $\Omega$ and this unusual line shape changes to Drude-like by increasing the chemical potential $|\mu |$, with width linear in $\mu$. The interband contribution at $T=0$ is a constant independent of $\Omega$ with a lower cutoff at $2\mu$. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap $\Delta$. At a large magnetic field $B$, the diagonal and Hall conductivities at small $\Omega$ become independent of $B$ but remain nonzero and show a structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, $E_0=\pm \Delta$, is field independent in sharp contrast to the conventional case.