Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator

Abstract

Graphene irradiated by a circularly polarized laser has been predicted to be a Floquet topological insulator showing a laser-induced quantum Hall effect. A circularly polarized laser also drives the system out of equilibrium resulting in non-thermal electron distribution functions that strongly affect transport properties. Results are presented for the Hall conductance for two different cases. One is for a closed system such as a cold-atomic gas where transverse drift due to non-zero Berry curvature can be measured in time of flight measurements. For this case the effect of a circularly polarized laser that has been switched on suddenly is studied. The second is for an open system coupled to an external reservoir of phonons. While for the former, the Hall conductance is far from the quantized limit, for the latter, coupling to a sufficiently low temperature reservoir of phonons is found to produce effective cooling, and thus an approach to the quantum limit, provided the frequency of the laser is large as compared to the band-width. For laser frequencies comparable to the band-width, strong deviations from the quantum limit of conductance is found even for a very low temperature reservoir, with the precise value of the Hall conductance determined by a competition between reservoir induced cooling and the excitation of photo-carriers by the laser. For the closed system, the electron distribution function is determined by the overlap between the initial wavefunction and the Floquet states which can result in a Hall conductance which is opposite in sign to that of the open system.

Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator

“…Moreover from the edge state population, we give simple Landauer based arguments to estimate the conductance of the edge modes. In doing so we arrive at estimates that are consistent with a Kubo formalism computation of the dc Hall conductance of a bulk system with no boundaries 20,25 . Thus even though the conductance is not Ce 2 /h for resonant lasers due to nonequilibrium occupation of bands, we uncover a bulk-boundary correspondence that persists even in the nonequilibrium system, where the Hall response for a spatially extended system without edges is of the same magnitude as the transport via edge states populated in a nonequilibrium way for precisely the same system but now with spatial boundaries.…”

“…For the latter, a proper Kubo formula or Landauer formalism approach needs to be employed. Employing Kubo formalism, one finds that the Hall current is determined by topological properties such as the time-averaged Berry curvature, but now weighted by the occupation probabilities of the quasi-energy bands 20 . The average current density on the other hand is far more sensitive to microscopic details, and can be probed using other methods such as sensitive magnetometers like SQUIDs that respond to the local magnetization generated by local currents 29,30 .…”

“…In fact FTIs are extremely rich, showing a variety of topological phases as the amplitude, frequency, and polarization of the periodic drive is varied [17][18][19][20] .…”

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

“…Going beyond the single-particle level, an important challenge is to understand how the properties of the AFAI change in the presence of interactions. An exciting possibility is to obtain a topologically nontrivial steady state for an interacting, periodically driven system [15][16][17]19,20]. The common wisdom dictates that a periodically driven system with dispersive modes is doomed to evolve into a highly random state that is essentially an infinite temperature state as far as any finite-order correlation functions are concerned [51,[59][60][61][62][63].…”

“…III, it is straightforward to check that the current [Eq. (16)] is indeed quantized. In that model, all bulk states have ∂ε j =∂θ x ¼ 0, whereas for all the extended states along the upper edge, ∂ε j =∂θ x ¼ 2π=NT, where N is the number of unit cells along the perimeter of the cylinder.…”