Quantized Adiabatic Transport In Momentum Space

Ho, Derek Y. H.; Gong, Jiangbin

doi:10.1103/physrevlett.109.010601

Cited by 120 publications

(155 citation statements)

References 38 publications

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“…It has also inspired numerous proposals and experiments for realizing topologically non-trivial bands using light, 4 sound, 5,6 and other types of waves. 7 According to the topological bulk-edge correspondence principle, 8 topologically nontrivial bandstructures imply the existence of topologically-protected edge states, whose unique transport properties may have applications in many fields.…”

Section: Introductionmentioning

confidence: 99%

Exceptional points in a non-Hermitian topological pump

et al. 2017

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We investigate the effects of non-Hermiticity on topological pumping, and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear. We show that this can be understood in terms of the effects of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally, in a non-Hermitian microwave network containing variable gain amplifiers.

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Section: Introductionmentioning

confidence: 99%

Exceptional points in a non-Hermitian topological pump

et al. 2017

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“…One proposal to attain a controllable topological phase is to introduce a driving field (time periodic term) into a system. By using Floquet theory [23][24][25][26], it can be shown that such a driving field can modify the topology of the system's band structure. This method has been used to generate several topological phases such as Floquet topological insulators [27,28] and Floquet Weyl semimetals [29].…”

Section: Introductionmentioning

confidence: 99%

Generating controllable type-II Weyl points via periodic driving

Bomantara

Gong

2016

Phys. Rev. B

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Type-II Weyl semimetals are a novel gapless topological phase of matter discovered recently in 2015. Similar to normal (type-I) Weyl semimetals, type-II Weyl semimetals consist of isolated band touching points. However, unlike type-I Weyl semimetals which have a linear energy dispersion around the band touching points forming a three dimensional (3D) Dirac cone, type-II Weyl semimetals have a tilted cone-like structure around the band touching points. This leads to various novel physical properties that are different from type-I Weyl semimetals. In order to study further the properties of type-II Weyl semimetals and perhaps realize them for future applications, generating controllable type-II Weyl semimetals is desirable. In this paper, we propose a way to generate a type-II Weyl semimetal via a generalized Harper model interacting with a harmonic driving field. When the field is treated classically, we find that only type-I Weyl points emerge.However, by treating the field quantum mechanically, some of these type-I Weyl points may turn into type-II Weyl points. Moreover, by tuning the coupling strength, it is possible to control the tilt of the Weyl points and the energy difference between two Weyl points, which makes it possible to generate a pair of mixed Weyl points of type-I and type-II. We also discuss how to physically distinguish these two types of Weyl points in the framework of our model via the Landau level structures in the presence of an artificial magnetic field. The results are of general interest to quantum optics as well as ongoing studies of Floquet topological phases.

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“…Topological invariants have gained considerable interest in solid state physics and related fields through their application to the quantum Hall effect [1,2], topological insulators [3][4][5][6], and more recently, Floquet-Bloch systems [7][8][9][10][11][12][13][14][15][16][17][18][19]. While the relevant topological invariants for the quantum Hall effect are the Chern numbers of the respective bands of the Hamiltonian, the invariants for Floquet-Bloch systems are constructed for unitary maps that are derived from the time propagator of the periodically driven system.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of theW₃topological invariant and application to Floquet–Bloch systems

Höckendorf¹,

Alvermann²,

Fehske³

2017

J. Phys. A: Math. Theor.

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We introduce an efficient algorithm for the computation of the W 3 invariant of general unitary maps, which converges rapidly even on coarse discretization grids. The algorithm does not require extensive manipulation of the unitary maps, identification of the precise positions of degeneracy points, or fixing the gauge of eigenvectors. After construction of the general algorithm, we explain its application to the 2 + 1 dimensional maps that arise in the Floquet-Bloch theory of periodically driven two-dimensional quantum systems. We demonstrate this application by computing the W 3 invariant for an irradiated graphene model with a continuously modulated Hamilton operator, where it predicts the number of anomalous edge states in each gap.

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Quantized Adiabatic Transport In Momentum Space

Cited by 120 publications

References 38 publications

Exceptional points in a non-Hermitian topological pump

Exceptional points in a non-Hermitian topological pump

Generating controllable type-II Weyl points via periodic driving

Efficient computation of theW₃topological invariant and application to Floquet–Bloch systems

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Quantized Adiabatic Transport In Momentum Space

Cited by 120 publications

References 38 publications

Exceptional points in a non-Hermitian topological pump

Exceptional points in a non-Hermitian topological pump

Generating controllable type-II Weyl points via periodic driving

Efficient computation of theW3topological invariant and application to Floquet–Bloch systems

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Product

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Efficient computation of theW₃topological invariant and application to Floquet–Bloch systems