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Floquet topological insulator in semiconductor quantum wells

Nature Physics volume 7, pages 490–495 (2011)Cite this article

Abstract

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, and potential applications ranging from semiconductor spintronics to topological quantum computation. Despite recent advancements in the field, our ability to control topological transitions remains limited, and usually requires changing material or structural properties. We show, using Floquet theory, that a topological state can be induced in a semiconductor quantum well, initially in the trivial phase. This can be achieved by irradiation with microwave frequencies, without changing the well structure, closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. 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, the Floquet topological insulator, introduced in this paper.

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Figure 1: Inducing an FTI from a trivial insulator.
Figure 2: A topological Floquet band.
Figure 3: The geometrical condition for creating topological quasi-energy bands.
Figure 4: Edge states in the quasi-energy spectrum.
Figure 5: Time dependence of the edge states.

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Acknowledgements

We thank J. Avron, A. Auerbach, E. Berg, A. Bernevig, J. Eisenstein, L. Fidkowski, V. Gurarie, I. Klich, and A. Polkovnikov for illuminating conversations. This research was supported by DARPA (G.R., V.G.), NSF grants PHY-0456720 and PHY-0803371 (G.R., N.H.L.). N.H.L. acknowledges the financial support of the Rothschild Foundation and the Gordon and Betty Moore Foundation.

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Authors and Affiliations

  1. Institute of Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

    Netanel H. Lindner & Gil Refael

  2. Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

    Netanel H. Lindner & Gil Refael

  3. Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA

    Victor Galitski

  4. Department of Physics, Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA

    Victor Galitski

Authors
  1. Netanel H. Lindner
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Contributions

N.H.L., G.R. and V.G. contributed to the conceptual developments. N.H.L. carried out the mathematical analysis.

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Correspondence to Netanel H. Lindner.

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Lindner, N., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nature Phys 7, 490–495 (2011). https://doi.org/10.1038/nphys1926

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