Time-resolved Hall conductivity of pulse-driven topological quantum systems

Abstract

We address the question of how the time-resolved bulk Hall response of a two-dimensional honeycomb lattice develops when driving the system with a pulsed perturbation. A simple toy model that switches a valley Hall signal by breaking inversion symmetry is studied in detail for slow quasiadiabatic ramps and sudden quenches, obtaining an oscillating dynamical response that depends strongly on doping and time-averaged values that are determined both by the out of equilibrium occupations and the Berry curvature of the final states. On the other hand, the effect of irradiating the sample with a circularly-polarized pump pulse that breaks time reversal symmetry and thus ramps the system into a nontrivial topological regime is probed. Even though there is a nonquantized average signal due to the breakdown of the Floquet adiabatical picture, some features of the photon-dressed topological bands are revealed to be present even in a few femtosecond timescale. Small frequency oscillations during the transient response evidence the emergence of dynamical Floquet gaps which are consistent with the instantaneous amplitude of the pump envelope. On the other hand, a characteristic heterodyning effect is manifested in the model. The presence of a remnant Hall response for ultrashort pulses that contain only a few periods of the radiation field is briefly discussed.