Unconventional pairing in three-dimensional topological insulators with a warped surface state

Abstract

We study the effect of the Fermi surface anisotropy (hexagonal warping) on the superconducting pair potential, induced in a three-dimensional topological insulator (TI) by proximity with an s-wave superconductor (S) in presence of a magnetic moment of a nearby ferromagnetic insulator (FI). In the previous studies, similar problem was treated with a simplified Hamiltonian, describing an isotropic Dirac cone dispersion. This approximation is only valid near the Dirac point. However, in topological insulators, the chemical potential often lies well above this point, where the Dirac cone is strongly anisotropic and its constant energy contour has a snowflake shape. Taking into account this shape, we show that a very exotic pair potential is induced on the topological insulator surface. Based on the symmetry arguments we also discuss the possibility of a supercurrent flowing along the S/FI interface, when an S/FI hybrid structure is formed on the TI surface.

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References

  1. 1.

    M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

    ADS  Article  Google Scholar 

  2. 2.

    X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).

    ADS  Article  Google Scholar 

  3. 3.

    G. Tkachov and E. M. Hankiewicz, Phys. Status Solidi 250, 215 (2013).

    Article  Google Scholar 

  4. 4.

    X.-L. Qi, R. Li, J. Zang, and S.-C. Zhang, Science 323, 1184 (2009).

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    C. W. J. Beenakker, Ann. Rev. Condens. Matter Phys. 4, 113 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    T. D. Stanescu, J. D. Sau, R. M. Lutchyn, and S. Das Sarma, Phys. Rev. B 81, 241310(R) (2010).

  7. 7.

    A. M. Black-Schaffer, Phys. Rev. B 83, 060504(R) (2011).

    ADS  Article  Google Scholar 

  8. 8.

    A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964).

    Google Scholar 

  9. 9.

    Y. Asano and Y. Tanaka, Phys. Rev. B 87, 104513 (2013).

    ADS  Article  Google Scholar 

  10. 10.

    M. Snelder, A. A. Golubov, Y. Asano, and A. Brinkman, J. Phys.: Condens. Matter 27, 315701 (2015); M. Veldhorst, M. Hoek, M. Snelder, H. Hilgenkamp, A. A. Golubov, and A. Brinkman, Phys. Rev. B 90, 035428 (2014); M. Snelder, C. G. Molenaar, Y. Pan, D. Wu, Y. K. Huang, A. de Visser, A. A. Golubov, W. G. van der Wiel, H. Hilgenkamp, M. S. Golden, and A. Brinkman, Supercond. Sci. Technol. 27, 104001 (2014).

    ADS  Google Scholar 

  11. 11.

    P. Burset, B. Lu, G. Tkachov, Y. Tanaka, E. M. Hankiewicz, and B. Trauzettel, Phys. Rev. B 92, 205424 (2015).

    ADS  Article  Google Scholar 

  12. 12.

    M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).

    ADS  Article  Google Scholar 

  13. 13.

    V. L. Berezinskii, JETP Lett. 20, 287 (1974).

    ADS  Google Scholar 

  14. 14.

    A. Balatsky and E. Abrahams, Phys. Rev. B 45, 13125 (1992).

    ADS  Article  Google Scholar 

  15. 15.

    M. Vojta and E. Dagotto, Phys. Rev. B 59, R713 (1999).

    ADS  Article  Google Scholar 

  16. 16.

    Y. Fuseya, H. Kohno, and K. Miyake, J. Phys. Soc. Jpn. 72, 2914 (2003).

    ADS  Article  Google Scholar 

  17. 17.

    F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005).

    ADS  Article  Google Scholar 

  18. 18.

    Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98, 037003 (2007).

    ADS  Article  Google Scholar 

  19. 19.

    Y. Tanaka, Y. Tanuma, and A. A. Golubov, Phys. Rev. B 76, 054522 (2007).

    ADS  Article  Google Scholar 

  20. 20.

    J. Linder, T. Yokoyama, Y. Tanaka, Y. Asano, and A. Sudbo, Phys. Rev. B 77, 174505 (2008).

    ADS  Article  Google Scholar 

  21. 21.

    Y. Tanaka, T. Yokoyama, and N. Nagaosa, Phys. Rev. Lett. 103, 107002 (2009).

    ADS  Article  Google Scholar 

  22. 22.

    I. V. Bobkova, A. M. Bobkov, A. A. Zyuzin, and M. Alidoust, Phys. Rev. B 94, 134506 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K.Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Science 325, 178 (2009).

    ADS  Article  Google Scholar 

  24. 24.

    K. Kuroda, M. Arita, K. Miyamoto, M. Ye, J. Jiang, A. Kimura, E. E. Krasovskii, E. V. Chulkov, H. Iwasawa, T. Okuda, K. Shimada, Y. Ueda, H. Namatame, and M. Taniguchi, Phys. Rev. Lett. 105, 076802 (2010).

    ADS  Article  Google Scholar 

  25. 25.

    M. Nomura, S. Souma, A. Takayama, T. Sato, T. Takahashi, K. Eto, K. Segawa, and Y. Ando, Phys. Rev. B 89, 045134 (2014).

    ADS  Article  Google Scholar 

  26. 26.

    S. V. Eremeev, G. Landolt, T. V. Menshchikova, et al., Nature Commun. 3, 635 (2012).

    Article  Google Scholar 

  27. 27.

    L. Fu, Phys. Rev. Lett. 103, 266801 (2009).

    ADS  Article  Google Scholar 

  28. 28.

    J. Linder, Y. Tanaka, T. Yokoyama, A. Sudbo, and N. Nagaosa, Phys. Rev. B 81, 184525 (2010).

    ADS  Article  Google Scholar 

  29. 29.

    K. N. Nesterov, M. Houzet, and J. S. Meyer, Phys. Rev. B 93, 174502 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    I. V. Tokatly, private communication.

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Correspondence to A. S. Vasenko.

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Vasenko, A.S., Golubov, A.A., Silkin, V.M. et al. Unconventional pairing in three-dimensional topological insulators with a warped surface state. Jetp Lett. 105, 497–501 (2017). https://doi.org/10.1134/S0021364017080082

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