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...

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities nimp. For dirty samples (250 ؋ 10 10 cm ؊2 < nimp < 400 ؋ 10 10 cm ؊2 ), the value of the minimum conductivity at low carrier density is indeed 4e 2 /h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on nimp, increasing to 8e 2 /h for nimp Ϸ 20 ؋ 10 10 cm ؊2 . A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.Boltzmann transport ͉ electron transport ͉ minimum conductivity

Kondo insulators are a particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological classification of emergent band structures for Kondo insulators and show that these materials may host three-dimensional topological insulating phases. We propose a general and practical prescription of calculating the Z(2) topological indices for various lattice structures. Experimental implications of the topological Kondo insulating behavior are discussed.