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 2µ. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap ∆. 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, E0 = ±∆, is field independent in sharp contrast to the conventional case.

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

“…(39)] partially overlap at high frequency, with the effect that the real part of σ xx (ω) displays the so-called Shubnikov-de Haas oscillations around the universal ac optical conductivity of graphene, σ g (the imaginary part, in turn, oscillates around zero). [8][9][10][11][12][13][14][15] The semi-classical conductivity is null, on the other hand, thus failing to describe the magneto-transport in neutral graphene.…”

“…8,11,31,41 Using the LL wavefunctions [Eq. (6)], we easily find the non-zero matrix elements to be, (28) where in the last line n, n = 0.…”

“…7 In the absence of disorder and other relaxation mechanisms (such as electron-phonon scattering), the conductivity of graphene (at zero magnetic field) would be exclusively determined by interband transitions. In the limit of no disorder, the optical conductivity of doped graphene, in the infrared region of the spectrum and at zero magnetic field, is given by [8][9][10][11][12][13][14][15] σ xx = σ g n F ( ω − 2E F ) ,…”

Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects

“…Electrodynamic properties of graphene, which have been studied both experimentally 31,32,33,34 and theoretically 5,15,16,24,28,29,35,36,37,38,39,40,41,42,43,44,45,46,47,48 , also demonstrate non-trivial features in the frequency dependent conductivity 15,24,28,35,48 , photon-assisted transport 36 , microwave and far-infrared response 29,37,38,39,40,41 , plasmons spectrum 42,43,44,45,46 , et cetera. New electromagnetic modes, specific only for the graphene system, have been also predicted 47,48 .…”

Fine structure constant and quantized optical transparency of plasmonic nanoarrays

“…( ) / w = = 2 4 is determined solely by universal constants 4,5 , and, consequently, graphene's absorption in the near-infrared is determined by the fine structure constant 6,7 , α. This behaviour was generalized later to any two-dimensional (2D) electronic system with a symmetric homogeneous spectrum 8 where absorption was shown to be quantized in units of πα.…”