Nonlinear current of strongly irradiated quantum Hall gas

Auerbach, Assa; Pai, G. Venketeswara

doi:10.1103/physrevb.76.205318

Cited by 39 publications

(21 citation statements)

References 35 publications

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“…The consequences of an AC-drive for quantum phase transitions have been investigated in a variety of models [24][25][26][27], such as the Dicke model [24] and the Ising model [25]. The modification of transport properties in periodically driven systems has been the subject of multiple studies, too [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Bukov

D’Alessio

Polkovnikov

2015

Advances in Physics

1,169

1,291

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We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper-Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer-Wolff transformation extending the latter to driven systems. PACS

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Section: Introductionmentioning

confidence: 99%

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Bukov

D’Alessio

Polkovnikov

2015

Advances in Physics

1,169

1,291

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“…[13] proposed to use a circularlypolarized light field to induce a Hall current in graphene. Another useful analogy for our work is the formation of zero-resistance state in Hall bars at low magnetic fields using RF radiation [14][15][16][17]. In our case, it is not the resistance of the bulk that vanishes, but rather the resistance of the edges, which becomes finite and universal upon application of the light field.…”

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confidence: 99%

Floquet topological insulator in semiconductor quantum wells

2011

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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...

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“…͑11͒. There are a few estimates of E c in the theoretical literature; 8,18 for the typical experimental density n =3ϫ 10 11 cm −2 , the highest estimate would be on the order 20 V/cm. Experimentally, while E c has not been measured, some of the results of Refs.…”

Section: Conclusion and Experimental Prospectsmentioning

confidence: 99%

“…At least two different microscopic mechanisms have been proposed to explain the microwave-induced resistance oscillations at lower microwave intensities and to produce the negative zero-field conductance assumed in the macroscopic model of ZRS: a "displacement mechanism," [8][9][10][11][12][13][14][15][16] in which the absorption of a microwave photon by an electron leads ͑for appropriate values of parameters͒ to a disorder-assisted displacement of the cyclotron orbit in an uphill direction with regard to the local dc electric field; and a "population mechanism," 17,18 in which absorption of the microwave photons leads to a population inversion in the partially filled Landau levels close to the Fermi level. Although these mechanisms may lead to quite different estimates for such parameters as the threshold microwave power or for the critical field E c at a given level of microwave irradiation, it appears that they give rise to qualitatively similar phenomenological models.…”

Section: Introductionmentioning

confidence: 99%

Microwave-induced zero-resistance states are not necessarily static

Finkler

Halperin

2009

Phys. Rev. B

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We study the eect of inhomogeneities in Hall conductivity on the nature of the Zero Resistance States seen in the microwave irradiated two-dimensional electron systems in weak perpendicular magnetic elds, and we show that time-dependent domain patterns may emerge in some situations.For an annular Corbino geometry, with an equilibrium charge density that varies linearly with radius, we nd a time-periodic non-equilibrium solution, which might be detected by a charge sensor, such as an SET. For a model on a torus, in addition to static domain patterns seen at high and low values of the equilibrium charge inhomogeneity, we nd that, in the intermediate regime, a variety of nonstationary states can also exist. We catalog the possibilities we have seen in our simulations. Within a particular phenomenological model, we show that linearizing the nonlinear charge continuity equation about a particularly simple domain wall conguration and analyzing the eigenmodes allows us to estimate the periods of the solutions to the full nonlinear equation.

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Nonlinear current of strongly irradiated quantum Hall gas

Cited by 39 publications

References 35 publications

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Floquet topological insulator in semiconductor quantum wells

Microwave-induced zero-resistance states are not necessarily static

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