Terahertz-frequency electronic transport in graphene

We calculate the room-temperature complex conductivity sigma(omega) of suspended and supported graphene at terahertz frequencies (100 GHz-10 THz) by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We consider a wide range of electron (n = 10(12)-10(13) cm(-2)) and impurity (N-i = 8 x 10(10)-2 x 10(12) cm(-2)) densities. For graphene supported on SiO2, there is excellent agreement between the calculation with clustered impurities and the experimentally measured sigma(omega). The choice of substrate (SiO2 or h-BN) is important at frequencies below 4 THz. We show that carrier scattering with substrate phonons governs transport in supported graphene for N-i/n < 0.1. Electron-impurity interactions dominate for N-i/n > 0.1, and transport enters the electron-hole puddle regime for N-i/n > 0.5. The simple Drude model, with an effective scattering rate Gamma and Drude weight D as parameters, fits the calculated sigma(omega) for supported graphene very well, owing to electron-impurity scattering. Gamma decreases with increasing n faster than n-1/2 and is insensitive to electron-electron interaction. Both electron-electron and electron-impurity interactions reduce the Drude weight D, and its dependence on n is sublinear.