Ballistic transport, chiral anomaly, and emergence of the neutral electron-hole plasma in graphene

Abstract

The process of coherent creation of particle -hole excitations by an electric field in graphene is quantitatively described using a dynamic "first quantized" approach. We calculate the evolution of current density, number of pairs and energy in ballistic regime using the tight binding model. The series in electric field strength E up to third order in both DC and AC are calculated. We show how the physics far from the two Dirac points enters various physical quantities in linear response and how it is related to the chiral anomaly. The third harmonic generation and the imaginary part of conductivity are obtained. It is shown that at certain time scale t nl ∝ E −1/2 the physical behaviour dramatically changes and the perturbation theory breaks down. Beyond the linear response physics is explored using an exact solution of the first quantized equations. While for small electric fields the I-V curve is linear characterized by the universal minimal resistivity σ = π/2(e 2 /h), at t > t nl the conductivity grows fast. The copious pair creation (with rate E 3/2 ), analogous to Schwinger's electron -positron pair creation from vacuum in QED, leads to creation of the electron -hole plasma at ballistic times of order t nl . This process is terminated by a relaxational recombination.

Interaction Induced Quantum Valley Hall Effect in Graphene

“…These include an anomalous integer quantum Hall effect (QHE) [4] and a puzzling finite ("minimal") dc conductivity at half filling [5], even in the absence of any dissipation and with a zero density of states. The theoretical determination of the zero-frequency limit of the optical conductivity and its dependence on interactions is still a challenge [6], in part due to the ambiguities associated with the ω → 0 limit in Kubo's formula. Attempts to include the effect of interactions in these calculations were recently made [7]; however, this effect disappears in the limit ω → 0.…”

Nonlinear electric transport in graphene with magnetic disorder

“…The effect of impurities on the electronic bands will depend on 1 Note however, that the nonlinear evolution found in Ref. [23] is identical to the one shown in Fig. 3.…”

“…We are interested in the dependency of the pair production rate and electric current on the intensity of the applied electric field. It is expected that under paramagnetic disorder the general picture of nonlinear transport is preserved * Alberto.Verga@univ-amu.fr [22,23], but that under magnetic order, this picture would change essentially as a consequence of localization [24]. In addition to the appearance of localized states, the opening of a gap induced by magnetically polarized impurities (magnetic state with spatial disorder), should significantly fade away the pair production, and consequently change the current-voltage characteristic.…”

“…In order to characterize the transport in this regime or in the presence of impurities, we monitor the pair creation rate [23],…”

Residual currents generated from vacuum by an electric field pulse in 2+1 dimensional QED models

“…The KE (1) conserves its form also in the tight-binding model of nearest neighbor interactions [5]. Here, primary the Fock representation is defined by the stationary in-vacuum state |in>.…”