Computational study of the two-terminal transport of Floquet quantum Hall insulators

Abstract

Periodic driving fields can induce topological phase transitions, resulting in Floquet topological phases with intriguing properties such as very large Chern numbers and unusual edge states. Whether such Floquet topological phases could generate robust edge state conductance much larger than their static counterparts is an interesting question. In this paper, working under the Keldysh formalism, we study two-lead transport via the edge states of irradiated quantum Hall insulators using the method of recursive Floquet-Green's functions.Focusing on a harmonically-driven Hofstadter model, we show that quantized Hall conductance as large as 8e 2 /h can be realized, but only after applying the so-called Floquet sum rule. To assess the robustness of edge state transport, we analyze the DC conductance, timeaveraged current profile and local density of states. It is found that co-propagating chiral edge modes are more robust against disorder and defects as compared with the remarkable counter-propagating edge modes, as well as certain symmetry-restricted Floquet edge modes.Furthermore, we go beyond the wide-band limit, which is often assumed for the leads, to study how the conductance quantization (after applying the Floquet sum rule) of Floquet edge states can be affected if the leads have finite bandwidths. These results may be useful for the design of transport devices based on Floquet topological matter.

Quantized Hall Conductance of a Single Atomic Wire: A Proposal Based on Synthetic Dimensions

“…1(a)]. Second, since the system is periodically driven (and thus belongs to the class of Floquetengineered systems [69][70][71][72]), transport properties rely on the underlying quasi-energy spectrum [73][74][75]. Altogether, the population of the Floquet eigenstates associated with the inner driven system is non-thermal, but it reflects the thermal population in the undriven reservoirs.…”

“…For a review of the Landauer-Büttiker formalism and of the recursive Green's function (RGF) method that was used to calculate the conductance shown in our paper, see Appendix A. A generalization of the RGF method [73][74][75]77], which is specifically tailored to treat timeperiodic systems, is presented in Appendix B.…”

“…As discussed in Refs. [75,91], the conductance of the effective model is then recovered by summing the transmissions T (m) α,β attributed to the different Floquet multiplicities…”

“…The Floquet sum rule in Eq. (11) allows one to recover the conductance of the effective (Floquet) time-independent model [75]. Specifically, the conductance is calculated by considering a two-terminal geometry, namely, by explicitly using the fact that the shaken channel is physically connected to two reservoirs [ Fig.…”

Floquet Majorana zero and π modes in planar Josephson junctions

“…To probe these transport quantities, we use the Floquet-Landauer formalism which has been utilized previously in related topological Floquet setups [30,[81][82][83][84][85]. We attach static leads to the 1D effective wire in the wide-band and weak-coupling limits.…”