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.

Spin-orbit coupling links a particle's velocity to its quantum mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin-orbit coupling originates from the movement of electrons in a crystal's intrinsic electric field, which is uniquely prescribed. In contrast, for ultracold atomic systems, the engineered "material parameters" are tuneable: a variety of synthetic spin-orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical status of spin-orbit coupling in ultracold atomic systems, discussing unique features that enable physics impossible in any other known setting.A particle's spin is quantized. In contrast to the angular momentum of an ordinary, i.e. classical, spinning top which can take on any value, measurements of an electron's spin angular momentum (or just "spin") along some direction can result in only two discrete values: ±ħ/2, commonly referred to as spin-up or spin-down. This internal degree of freedom has no classical counterpart; in contrast, a quantum particle's velocity is directly analogous to a classical particle's velocity. It is therefore no surprise that spin is a cornerstone to a variety of deeply quantum materials like quantum magnets 1 and topological insulators 2 . Spin-orbit coupling (SOC) intimately unites a particle's spin with its momentum, bringing quantum mechanics to the forefront; in materials, this often increases the energy scale at which quantum effects are paramount.The practical utility of any material is determined, not only by its intrinsic functional behavior, but also by the energy or temperature scale at which that behavior is present. For example, the quantum Hall effects -rare examples of truly quantum physics where the spin is largely irrelevant -are relegated to highly specialized laboratories because these phenomena manifest themselves only under extreme conditions -at liquid-helium temperatures and high magnetic fields 3,4 . The integer quantum Hall effect (IQHE) was the first observed topological insulator (TI), but it has a broken time-reversal symmetry. This is in contrast with a new class of topological insulators (see Box 1), which rely on SOC instead of magnetic fields for their quantum properties, and are expected to retain their quantumness up to room temperature 2 .As fascinating and unusual as the already existing topological world of spin-orbit-coupled systems is, all this physics is largely based on a noninteracting picture of independent electrons filling up a prescribed topological landscape. But there is clearly physics beyond this, as suggested by the fractional quantum Hall effect (FQHE) materials, where interactions between electrons yield phenomena qualitatively different from those encountered in IQHE. In FQHE systems, the charged excitations are essentially just fraction of an electron -with fractional charge -a new type of emergent excitation with no analogue elsewhere in physic...

We consider a many-body system of pseudo-spin-1/2 bosons with spin-orbit interactions, which couple the momentum and the internal pseudo-spin degree of freedom created by spatially varying laser fields. The corresponding single- particle spectrum is generally anisotropic and contains two degenerate minima at finite momenta. At low temperatures, the many-body system condenses into these minima generating a new type of entangled Bose-Einstein condensate. We show that in the presence of weak density-density interactions the many-body ground state is characterized by a twofold degeneracy. The corresponding many-body wave function describes a condensate of ``left-'' and ``right-moving'' bosons. By fine-tuning the parameters of the laser field, one can obtain a bosonic version of the spin-orbit coupled Rashba model. In this symmetric case, the degeneracy of the ground state is very large, which may lead to phases with nontrivial topological properties. We argue that the predicted new type of Bose-Einstein condensates can be observed experimentally via time-of-flight imaging, which will show characteristic multipeak structures in momentum distribution.Comment: published version, 10 pages, 4 figure

We examine how the properties of the Kondo insulators change when the symmetry of the underlying crystal field multiplets is taken into account. We employ the Anderson lattice model and consider its low-energy physics. We show that in a large class of crystal field configurations, Kondo insulators can develop a topological non-trivial ground-state. Such topological Kondo insulators are adiabatically connected to non-interacting insulators with unphysically large spin-orbit coupling, and as such may be regarded as interaction-driven topological insulators. We analyze the entanglement entropy of the Anderson lattice model of Kondo insulators by evaluating its entanglement spectrum. Our results for the entanglement spectrum are consistent with the surface state calculations. Lastly, we discuss the construction of the maximally localized Wannier wave functions for generic Kondo insulators.

This article reviews recent theoretical and experimental work on a new class of topological material-topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, → 0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the fourpoint correlator, C(t), for the classical and quantum kicked rotor -a textbook driven chaotic system -and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K → 0, while the OTOC's growth rate may decrease much slower showing higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time tE: transitioning from a time-independent value of t −1 ln C(t) at t < tE to its monotonous decrease with time at t > tE. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996); Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.Introduction. -One of the central goals in the study of quantum chaos is to establish a correspondence principle between classical and quantum dynamics of classically chaotic systems [1][2][3][4][5][6][7]. Several previous works [7][8][9][10][11] have attempted to recover fingerprints of classical chaos in quantum dynamics. In particular, Aleiner and Larkin [12] showed the existence of a semiclassical "quantum chaotic" regime attributed to the delay in the onset of quantum effects (due to weak localization) revealing the key measure of classical chaos -the Lyapunov exponent (LE). Recently, the subject of quantum chaos has been revived by the discovery of an unexpected conjecture that puts a bound on the growth rate of an outof-time-ordered four-point correlator (OTOC) [13,14]. OTOC was first introduced by Larkin and Ovchinnikov to quantify the regime of validity of quasi-classical methods in the theory of superconductivity [15]. The growth rate of OTOC appears to be closely related to LE. Recent works have proposed experimental protocols to probe OTOC in cold atom and cavity QED setups [16]. Several recent preprints have employed OTOC as a probe to characterize many-body-localized systems [17].