Terahertz-frequency electronic transport in graphene

Abstract

We calculate the room-temperature complex conductivity σ (ω) 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 × 10 10 -2 × 10 12 cm −2 ) densities. For graphene supported on SiO 2 , there is excellent agreement between the calculation with clustered impurities and the experimentally measured σ (ω). The choice of substrate (SiO 2 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 and Drude weight D as parameters, fits the calculated σ (ω) for supported graphene very well, owing to electron-impurity scattering. 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.

How good would the conductivity of graphene have to be to make single-layer-graphene metamaterials for terahertz frequencies feasible?

“…Consistent with this study, a detailed theoretical analysis for the room-temperature mobility indicated that impurity-free substrates (BN as well as SiO 2 ) would allow for ߬-values of about 0.5 ps, nearly independent of carrier density in the range from 1x10 12 to 1x10 13 cm -2 [32].…”

“…Mobility values varied considerably from sample to sample. With increasing carrier density, ߬ increased [32,33]. Chemical doping up to densities of 2.5x10 13 cm -2 was reported, the corresponding highest Fermi level being 0.585 eV [17].…”

“…In this case, theory [24] and experiment [29][30][31] show that for the comparatively low frequencies considered here ( ఠ ଶగ < 7 THz → ℏ߱ < 0.03 eV ), the interband contribution to the conductivity can be neglected against the intraband term. The complex sheet conductivity ߪ(߱, ‫ܧ‬ F , ߬) of doped or gated graphene can then be approximated by the Drude-type expression [20,24,32] 20,22], where ‫ݒ‬ F is the Fermi velocity ‫ݒ(‬ F = 10 m/s [25]). …”

Optical bistability of graphene in the terahertz range

“…(6)]. Using this and the similarity between the integrals I 31 ,I 33 and I 21 ,I 22 (replacing t ⊥ → √ 2t ⊥ ), we obtain the final expression for the current density given in the text.…”

“…In an experiment done in this type of graphene one would be in the regime ωτ 1. Indeed, a recent theoretical calculation [33] of the optical response of suspended graphene in the terahertz range, using ab initio methods, yielded a value of = 1/τ ∼ 0.8 THz which leads to 2πf/ ∼ 7.9.…”