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Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions

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Abstract

In this review, we mention about the theoretical achievement of physics of surface Andreev bound state (SABS) and odd-frequency pairing during this quarter century based on our research. Currently, topological superconductors with Majorana edge state have become a central issue in condensed matter physics. It is noted that Majorana edge state is nothing but a zero energy surface Andreev bound state (ZESABS) and the study of ZESABS has started in the context of the pairing symmetry of high Tc cuprate. We mention our obtained conductance formula of quasiparticle tunneling and Josephson current in unconventional superconductor junctions through ZESABS have already captured the essence of the charge transport profile via the Majorana fermion. We also mention that in the presence of ZESABS, odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave is hugely enhanced near the surface or interface. We further analyze the spectroscopy of the induced odd-frequency pairings by extending bulk-boundary correspondence in ZESABS. If we consider a semi-infinite superconductor with ZESABS, the induced odd-frequency pair amplitude can be expressed by a c-number defined in bulk, which we call spectral bulk-boundary correspondence. The odd-frequency pair amplitude is classified into singular part and regular one, the former part is proportional to \(\sim 1/z\) (z is a complex frequency) reflecting the presence of ZESABS, and the latter one is proportional to \(\sim z\). The coefficient of the latter one diverges at the topological phase transition point. Analyzing the spectral behavior of the odd-frequency pairing is useful to understand the critical phenomena near topological transition points.

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References

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

    Google Scholar 

  2. McMillan, W.L.: . Phys. Rev. 175, 537 (1968)

    ADS  Google Scholar 

  3. Caroli, C., de Gennes, P.G., Matricon, J.: . Phys. Lett. 9, 307 (1964)

    ADS  Google Scholar 

  4. Yu, L.: . Acta Phys. Sin. 21, 75 (1965)

    Google Scholar 

  5. Shiba, H.: . Prog. Theor. Phys. 40, 435 (1968)

    ADS  Google Scholar 

  6. Rusinov, A.: . Sov. Phys. JETP 29, 1101 (1969)

    ADS  Google Scholar 

  7. Blonder, G.E., Tinkham, M., Klapwijk, T.: . Phys. Rev. B 25, 4515 (1982)

    ADS  Google Scholar 

  8. Tanaka, Y., Kashiwaya, S.: . Phys. Rev. Lett. 74, 3451 (1995)

    ADS  Google Scholar 

  9. Kashiwaya, S., Tanaka, Y.: . Rep. Prog. Phys. 63, 1641 (2000)

    ADS  Google Scholar 

  10. Kashiwaya, S., Tanaka, Y., Koyanagi, M., Takashima, H., Kajimura, K.: . Phys. Rev. B 51, 1350 (1995)

    ADS  Google Scholar 

  11. Kashiwaya, S., Tanaka, Y., Terada, N., Koyanagi, M., Ueno, S., Alff, L., Takashima, H., Tanuma, Y., Kajimura, K.: . J. Phys. Chem. Solid 59, 2034 (1998)

    ADS  Google Scholar 

  12. Covington, M., Aprili, M., Paraoanu, E., Greene, L.H., Xu, F., Zhu, J., Mirkin, C.A.: . Phys. Rev. Lett. 79, 277 (1997)

    ADS  Google Scholar 

  13. Alff, L., Takashima, H., Kashiwaya, S., Terada, N., Ihara, H., Tanaka, Y., Koyanagi, M., Kajimura, K.: . Phys. Rev. B 55, R14757 (1997)

    ADS  Google Scholar 

  14. Wei, J.Y.T., Yeh, N.C., Garrigus, D.F., Strasik, M.: . Phys. Rev. Lett. 81, 2542 (1998)

    ADS  Google Scholar 

  15. Biswas, A., Fournier, P., Qazilbash, M.M., Smolyaninova, V.N., Balci, H., Greene, R.L.: . Phys. Rev. Lett. 88, 207004 (2002)

    ADS  Google Scholar 

  16. Chesca, B., Smilde, H.J.H., Hilgenkamp, H.: . Phys. Rev. B 77, 184510 (2008)

    ADS  Google Scholar 

  17. Kashiwaya, S., Tanaka, Y.: . Rep. Prog. Phys. 63(10), 1641 (2000)

    ADS  Google Scholar 

  18. Hu, C.R.: . Phys. Rev. Lett. 72, 1526 (1994)

    ADS  Google Scholar 

  19. Tanaka, Y., Yokoyama, T., Nagaosa, N.: . Phys. Rev. Lett. 103, 107002 (2009). https://doi.org/10.1103/PhysRevLett.103.107002

    Article  ADS  Google Scholar 

  20. Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 53, R11957 (1996)

    ADS  Google Scholar 

  21. Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 56, 892 (1997)

    ADS  Google Scholar 

  22. Furusaki, A., Tsukada, M.: . Phys. Rev. B 43, 10164 (1991)

    ADS  Google Scholar 

  23. Il’ichev, E., Grajcar, M., Hlubina, R., IJsselsteijn, R.P.J., Hoenig, H.E., Meyer, H.G., Golubov, A., Amin, M.H.S., Zagoskin, A.M., Omelyanchouk, A.N., Kupriyanov, M.Y.: . Phys. Rev. Lett. 86, 5369 (2001)

    ADS  Google Scholar 

  24. Testa, G., Sarnelli, E., Monaco, A., Esposito, E., Ejrnaes, M., Kang, D.J., Mennema, S.H., Tarte, E.J., Blamire, M.G.: . Phys. Rev. B 71, 134520 (2005)

    ADS  Google Scholar 

  25. Kwon, H., Sengupta, K., Yakovenko, V.: . Eur. Phys. J. B 37, 349 (2004)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. Tanaka, Y., Golubov, A.A., Kashiwaya, S., Ueda, M.: . Phys. Rev. Lett. 99, 037005 (2007)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  31. Sato, M., Tanaka, Y., Yada, K., Yokoyama, T.: . Phys.Rev.B 83, 224511 (2011)

    ADS  Google Scholar 

  32. Tanaka, Y., Sato, M., Nagaosa, N.: . J. Phys. Soc. Jpn. 81(1), 011013 (2012)

    ADS  Google Scholar 

  33. Tamura, S., Hoshino, S., Tanaka, Y.: . Phys. Rev. B 99, 184512 (2019)

    ADS  Google Scholar 

  34. Bruder, C.: . Phys. Rev. B 41, 4017 (1990)

    ADS  Google Scholar 

  35. Kashiwaya, S., Tanaka, Y., Koyanagi, M., Kajimura, K.: . Phys. Rev. B 53, 2667 (1996)

    ADS  Google Scholar 

  36. Haim, A., Berg, E., von Oppen, F., Oreg, Y.: . Phys. Rev. B 92, 245112 (2015)

    ADS  Google Scholar 

  37. Haim, A., Oreg, Y.: . Phys. Rep. 825, 1 (2019)

    ADS  MathSciNet  Google Scholar 

  38. Yang, J., Hu, C.R.: . Phys. Rev. B 50, 16766 (1994)

    ADS  Google Scholar 

  39. Yamashiro, M., Tanaka, Y., Tanuma, Y., Kashiwaya, S.: . J. Phys. Soc. Jpn. 67, 3224 (1998)

    ADS  Google Scholar 

  40. Yamashiro, M., Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 56, 7847 (1997)

    ADS  Google Scholar 

  41. Tanaka, Y., Tanuma, Y., Kuroki, K., Kashiwaya, S.: . J. Phys. Soc. Jpn 71, 2102 (2002)

    ADS  Google Scholar 

  42. Kashiwaya, S., Kashiwaya, H., Kambara, H., Furuta, T., Yaguchi, H., Tanaka, Y., Maeno, Y.: . Phys. Rev. Lett. 107, 077003 (2011)

    ADS  Google Scholar 

  43. Nagato, Y., Nagai, K.: . Phys. Rev. B 51, 16254 (1995)

    ADS  Google Scholar 

  44. Matsumoto, M., Shiba, H.: . J. Phys. Soc. Jpn. 64, 4867 (1995)

    ADS  Google Scholar 

  45. Fogelström, M., Rainer, D., Sauls, J.A.: . Phys. Rev. Lett. 79, 281 (1997). https://doi.org/10.1103/PhysRevLett.79.281

    Article  ADS  Google Scholar 

  46. Eschrig, M.: . Phys. Rev. B 61, 9061 (2000)

    ADS  Google Scholar 

  47. Barash, Y., Svidzinsky, A., Burkhardt, H.: . Phys. Rev. B 55, 15282 (1997)

    ADS  Google Scholar 

  48. Tanuma, Y., Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 64, 214519 (2001)

    ADS  Google Scholar 

  49. Tanuma, Y., Tanaka, Y., Yamashiro, M., Kashiwaya, S.: . Phys. Rev. B 57, 7997 (1998)

    ADS  Google Scholar 

  50. Josephson, B.: . Phys. Lett. 1, 251 (1962)

    ADS  Google Scholar 

  51. Kohmoto, A., Tsukada, M.: . Sold State Commun. 78, 249 (1991)

    Google Scholar 

  52. Beenakker, C.W.J., van Houten, H.: . Phys. Rev. Lett. 66, 3056 (1991)

    ADS  Google Scholar 

  53. Ambegaokar, V., Baratoff, A.: . Phys. Rev. Lett. 10, 486 (1963)

    ADS  Google Scholar 

  54. Kulik, I., Omelyanchuk, A.: . Sov. J. Low Temp. Phys. 4, 142 (1978)

    Google Scholar 

  55. Geshkenbein, V.B., Larkin, A.I., Barone, A.: . Phys. Rev. B 36, 235 (1987)

    ADS  Google Scholar 

  56. Sigrist, M., Rice, T.: . J. Phys. Soc. Jpn. 61, 4283 (1992)

    ADS  Google Scholar 

  57. Wollman, D.A., van Harlingen, D.J., Lee, W.C., Ginsberg, D.M., Leggett, A.J.: . Phys. Rev.Lett. 71, 2134 (1993)

    ADS  Google Scholar 

  58. Harlingen, D.J.V.: . Rev. Mod. Phys. 67, 515 (1995)

    ADS  Google Scholar 

  59. Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 53, 9371 (1996)

    ADS  Google Scholar 

  60. Barash, Y.S., Burkhardt, H., Rainer, D.: . Phys. Rev. Lett. 77, 4070 (1996)

    ADS  Google Scholar 

  61. Kirkpatrick, T.R., Belitz, D.: . Phys. Rev. Lett. 66, 1533 (1991)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  63. Abrahams, E., Balatsky, A., Scalapino, D.J., Schrieffer, J.R.: . Phys. Rev. B 52, 1271 (1995)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  65. Coleman, P., Georges, A., Tsvelik, A.M.: . J. Phys. Condens. Matter 9, 345 (1997)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  67. Shigeta, K., Onari, S., Yada, K., Tanaka, Y.: . Phys. Rev. B 79, 174507 (2009)

    ADS  Google Scholar 

  68. Kusunose, H., Fuseya, Y., Miyake, K.: . J. Phys. Soc. Jpn. 80, 054702 (2011)

    ADS  Google Scholar 

  69. Fominov, Y.V., Tanaka, Y., Asano, Y., Eschrig, M.: . Phys. Rev. B 91, 144514 (2015)

    ADS  Google Scholar 

  70. Bergeret, F.S., Volkov, A.F., Efetov, K.B.: . Phys. Rev. Lett. 86, 4096 (2001)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  72. Eschrig, M., Löfwander, T., Champel, T., Cuevas, J., Schön, G.: . J. Low Temp. Phys. 147, 457 (2007)

    ADS  Google Scholar 

  73. Tanaka, Y., Kashiwaya, S.: . Phys. Rev. B 70, 012507 (2004)

    ADS  Google Scholar 

  74. Tanaka, Y., Kashiwaya, S., Yokoyama, T.: . Phys. Rev. B 71, 094513 (2005)

    ADS  Google Scholar 

  75. Tanaka, Y., Asano, Y., Golubov, A.A., Kashiwaya, S.: . Phys. Rev. B 72, 140503(R) (2005)

    ADS  Google Scholar 

  76. Lutchyn, R.M., Sau, J.D., Sarma, S.D.: . Phys. Rev. Lett. 105, 077001 (2010)

    ADS  Google Scholar 

  77. Oreg, Y., Refael, G., von Oppen, F.: . Phys. Rev. Lett. 105, 177002 (2010)

    ADS  Google Scholar 

  78. Gurarie, V.: . Rev, Phys. B 83, 085426 (2011). https://doi.org/10.1103/PhysRevB.83.085426

    Article  Google Scholar 

  79. Daido, A., Yanase, Y.: . Phys. Rev. B 100, 174512 (2019). https://doi.org/10.1103/PhysRevB.100.174512

    Article  ADS  Google Scholar 

  80. Kitaev, A.Y.: . Phys. Usp. 44(10S), 131 (2001). https://doi.org/10.1070/1063-7869/44/10s/s29

    Article  ADS  Google Scholar 

  81. Sachdev, S.: Quantum Phase Transitions, 2nd edn. Cambridge University Press, Cambridge (2011)

    MATH  Google Scholar 

  82. Mourik, V., Zuo, K., Frolov, S., Bakkers, E.P.A.M., Plissard, S., Kouwenhoven, L.P.: . Science 336, 1003 (2012)

    ADS  Google Scholar 

  83. Fisher, D.S., Lee, P.A.: . Phys. Rev. B 23, 6851 (1981). https://doi.org/10.1103/PhysRevB.23.6851

    Article  ADS  MathSciNet  Google Scholar 

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Funding

This work was supported by a Grant-in-Aid for a Grant-in-Aid for Scientific Research A (KAKENHI Grant No. JP20H00131), Scientific Research B (KAKENHI Grant No. JP18H01176) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan (MEXT) and JSPS Core-to-Core program “Oxide Superspin” international network.

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  1. Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan

    Yukio Tanaka & Shun Tamura

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  1. Yukio Tanaka
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  2. Shun Tamura
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Correspondence to Yukio Tanaka.

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Tanaka, Y., Tamura, S. Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions. J Supercond Nov Magn 34, 1677–1694 (2021). https://doi.org/10.1007/s10948-020-05672-2

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