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Floquet topological insulator in semiconductor quantum wells

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.

References

  1. Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    ADS  Article  Google Scholar 

  2. König, M. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    ADS  Article  Google Scholar 

  3. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).

    ADS  Article  Google Scholar 

  4. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).

    ADS  Article  Google Scholar 

  5. Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3, Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).

    ADS  Article  Google Scholar 

  6. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    ADS  Article  Google Scholar 

  7. Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    ADS  MathSciNet  Article  Google Scholar 

  8. Žutić, I., Fabian, J. & Das Sarma, S. Spintronics: Fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    ADS  Article  Google Scholar 

  9. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  10. Kitagawa, T., Rudner, M. S., Berg, E. & Demler, E. Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010).

    ADS  Article  Google Scholar 

  11. Sörensen, A. S., Demler, E. & Lukin, M. D. Fractional quantum Hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).

    ADS  Article  Google Scholar 

  12. Lin, Y. J., Compton, R. L., Jimenez-Garcia, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009).

    ADS  Article  Google Scholar 

  13. Stanescu, T. D., Galitski, V., Vaishnav, J. Y., Clark, C. W. & Das Sarma, S. Topological insulators and metals in atomic optical lattices. Phys. Rev. A 79, 053639 (2009).

    ADS  Article  Google Scholar 

  14. Oka, T. & Aoki, H. Photovoltaic Hall effect in graphene. Phys. Rev. B 79, 081406(R) (2009).

    ADS  Article  Google Scholar 

  15. Mani, R. G. et al. Zero-resistance states induced by electromagnetic-wave excitation in GaAs/AlGaAs heterostructures. Nature 420, 646–650 (2002).

    ADS  Article  Google Scholar 

  16. Zudov, M. A., Du, R. R., Pfeiffer, L. N. & West, K. W. Evidence for a new dissipationless effect in 2D electronic transport. Phys. Rev. Lett. 90, 046807 (2003).

    ADS  Article  Google Scholar 

  17. Auerbach, A. & Pai, G. V. Nonlinear current of strongly irradiated quantum Hall gas. Phys. Rev. B 76, 205318 (2007).

    ADS  Article  Google Scholar 

  18. Dmitriev, I. A., Vavilov, M. G., Aleiner, I. L., Mirlin, A. D. & Polyakov, D. G. Theory of microwave-induced oscillations in the magnetoconductivity of a two-dimensional electron gas. Phys. Rev. B 71, 115316 (2005).

    ADS  Article  Google Scholar 

  19. Inoue, J. & Tanaka, A. Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems. Phys. Rev. Lett. 105, 017401 (2010).

    ADS  Article  Google Scholar 

  20. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the ‘parity anomaly’. Phys. Rev. Lett. 61, 2015–2018 (1988).

    ADS  MathSciNet  Article  Google Scholar 

  21. Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008).

    ADS  Article  Google Scholar 

  22. Kitaev, A. Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22–30; (2009) preprint at http://arxiv.org/abs/0901.2686.

  23. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    ADS  Article  Google Scholar 

  24. Novik, E. G. et al. Band structure of semimagnetic Hg1−yMnyTe quantum wells. Phys. Rev. B 72, 035321 (2005).

    ADS  Article  Google Scholar 

  25. Zhang, X. C., Ortner, K., Pfeuffer-Jeschke, A., Becker, C. R. & Landwehr, G. Effective g factor of n-type HgTe/Hg1−xCdxTe single quantum wells. Phys. Rev. B 69, 115340 (2004).

    ADS  Article  Google Scholar 

  26. Willatzen, M., Cardona, M. & Christensen, N. E. Spin–orbit coupling parameters and electron g factor of II–VI zinc-blende materials. Phys. Rev. B. 51, 17992–17994 (1995).

    ADS  Article  Google Scholar 

  27. Rothe, D. G. et al. Fingerprint of different spin–orbit terms for spin transport in HgTe quantum wells. New J. Phys. 12, 065012 (2010).

    ADS  Article  Google Scholar 

  28. Kitagawa, T., Berg, E., Rudner, M. & Demle, E. Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010).

    ADS  Article  Google Scholar 

  29. Robertson, A. & Galitski, V. M. Nonequilibrium enhancement of Cooper pairing in cold fermion systems. Phys. Rev. A 80, 063609 (2009).

    ADS  Article  Google Scholar 

  30. Eliashberg, G. M. Film superconductivity stimulated by a high-frequency field. JETP Lett. 11, 114–116 (1970).

    ADS  Google Scholar 

  31. Eliashberg, G. M. in Nonequilibrium Superconductivity (eds Langenberg, D. N. & Larkin, A. I.) (North-Holland, 1986).

    Google Scholar 

  32. Glazman, L. I. Resonant excitation of carriers in a semiconductor by a high-power laser pulse. Sov. Phys. JETP 53, 178–181 (1981).

    Google Scholar 

  33. Glazman, L. I. Kinetics of electrons and holes in direct gap seminconductors photoexcited by high intensity pulses. Sov. Phys.—Semicond.-USSR 17, 494–498 (1983).

    Google Scholar 

Download references

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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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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The authors declare no competing financial interests.

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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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