Optically Engineering the Topological Properties of a Spin Hall Insulator

Abstract

Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for the helical edge state of a spin Hall insulator in the presence of monochromatic circularly polarized light. The inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity-dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signalling a change in the topological properties. The connection with Thouless' charge pumping and nonequilibrium zitterbewegung is discussed, together with possible experiments.

Floquet topological insulators

“…In particular, this quantization still survives for elliptic polarization, upon addition of an inversion symmetry breaking term and/or in presence of orbital effects, see supplementary material of Ref. [31]. Finally, this quantization is fairly general in the adiabatic limit where it can be deduced [46] from the GoldstoneWilczek formula [47].…”

“…Besides, it is natural to use photons to probe topological phases and their edge/surface states. We have studied a QSH state and its one-dimensional helical edge state in a circularly polarized radiation field [31]. Using Floquet theory, we have demonstrated that the photocurrent and the magnetization are ruled by the very same unit vector, whose winding number determines a topological invariant for the system.…”

“…To estimate the typical induced photocurrent, we recall that the | | g ω regime is realized usually (and note that larger values of ω are beneficial for neglecting the vector potential), and for a radiation field with magnetic field strength of the order of (for a 1 micron perimeter) is within the detectability limit of an ac SQUID [31].…”

“…Then in Section 3 we describe how non-trivial topological phases can be created by shining light on a trivial insulator or on semi-metallic graphene. Section 4 describes our work on the photocurrent generated by shining an electromagnetic wave onto the helical edge states of a QSH insulator [31]. Finally, Section 5 reviews related works on the photocurrent generation in the surface states of 3D topological insulators [32,33].…”

Topological Floquet spectrum in three dimensions via a two-photon resonance

“…The Floquet spectrum of a periodically driven system was shown to exhibit a variety of topological phases 7 . For instance, graphene is expected to exhibit a quantum Hall effect when subjected to radiation 9,12,13 ; a spin-orbit coupled semiconductor heterostructure (such as HgTe/CdTe wells), can be turned topological using microwave-teraHertz radiation 10 , and vice versa 14,15 .…”