Floquet topological insulator in semiconductor quantum wells

Abstract

Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride -cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, Floquet topological insulator, introduced in this paper.Topological phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations [1,2], and potential applications ranging from semiconductor spintronics [3] to topological quantum computation [4]. The discovery of topological insulators in solid-state devices such as HgTe/CdTe quantum wells [5,6], and in materials such as Bi 2 Te 3 , Bi 2 Sn 3 [7-9] brings us closer to employing the unique properties of topological phases in technological applications.Despite this success, however, the choice of materials that exhibit these unique topological properties remains rather scarce. In most cases we have to rely on serendipity in looking for topological materials in solidstate structures and our means to engineer Hamiltonians there are very limited. Therefore, to develop new methods to achieve and control topological structures at will would be of great importance.Our work demonstrates that such new methods are indeed possible in non-equilibrium, where external timedependent perturbations represent a rich and versatile resource that can be utilized to achieve topological spectra in systems that are topologically trivial in equilibrium. In particular, we show that periodic-in-time perturbations may give rise to new differential operators with topological insulator spectra, dubbed Floquet topological insulators (FTI), that exhibit chiral edge currents in nonequilibrium and possess other hallmark phenomena associated with topological phases. These ideas, put together with the highly developed technology for controlling lowfrequency electromagnetic modes, can enable devices in which fast switching of edge state transport is possible. Moreover, the spectral properties of the edge states, i.e., their velocity, and the bandgap of the bulk insulator, can be easily controlled. On a less applied perspective, the fast formation of the Floquet topological insulators in response to the external field opens a path to study quench dynamics of topological states in solid-state devices.The Floquet topological insulators discussed here share many features discussed in some previous works: The idea of achieving topological states in a periodic Hamilt...

Observation of topologically protected bound states in photonic quantum walks

“…The controllability of our system allows us to make small changes to the Hamiltonian and demonstrate the robustness of these bound states. Finally, using the quantum walk, we can access the dynamics of strongly driven systems far from the static or adiabatic regimes [17][18][19] , to which most previous work on topological phases has been restricted. In this regime, we discover a topologically protected pair of non-degenerate bound states, a phenomenon that is unique to periodically driven systems.…”

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 .…”

Selective scattering between Floquet–Bloch and Volkov states in a topological insulator

“…The strong time-periodic potential of intense laser light can be used to generate hybrid photon-electron states. Interaction of light with Bloch states leads to Floquet-Bloch states, which are essential in realizing new photo-induced quantum phases [6][7][8] . Similarly, dressing of free-electron states near the surface of a solid generates Volkov states, which are used to study nonlinear optics in atoms and semiconductors 9 .…”