Advertisement

JETP Letters

, Volume 103, Issue 11, pp 728–738 | Cite as

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

  • M. Yu. KaganEmail author
Scientific Summaries

Abstract

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. P. Drozdov, M. I. Eremets, and I. A. Troyan, Nature 525, 73 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    M. I. Eremets, I. A. Troyan, and A. P. Drozdov, arXiv:1601.04479 [cond-matsupr-con] (2016).Google Scholar
  3. 3.
    Y. Wang and Y. Ma, J. Chem. Phys. 140, 040901 (2014).ADSCrossRefGoogle Scholar
  4. 4.
    D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, and T. Cui, Sci. Rep. 4, 6968 (2014).ADSCrossRefGoogle Scholar
  5. 5.
    Y. Liu, D. Duan, F. Tian, D. Li, X. Sha, Z. Zhao, H. Zhang, G. Wu, H. Yu, B. Liu, and T. Cui, arXiv: 1503.08587 [cond-matsupr-con] (2015).Google Scholar
  6. 6.
    J. C. Hubbard, Proc. R. Soc. London A 276, 238 (1963).ADSCrossRefGoogle Scholar
  7. 7.
    S. P. Shubin and S. V. Vonsovsky, Phys. Z. Sowjetunion 7, 292 (1935).Google Scholar
  8. 8.
    S. P. Shubin and S. V. Vonsovsky, Phys. Z. Sowjetunion 10, 348 (1936).Google Scholar
  9. 9.
    W. Kohn and J. M. Luttinger, Phys. Rev. Lett. 15, 524 (1965).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Fay and A. Layzer, Phys. Rev. Lett. 20, 187 (1968).ADSCrossRefGoogle Scholar
  11. 11.
    M. Yu. Kagan, M. M. Korovushkin, and V. A. Mitskan, Phys. Usp. 58, 733 (2015).ADSCrossRefGoogle Scholar
  12. 12.
    M. Yu. Kagan, Modern Trends in Superconductivity and Superfluidity, Lect. Notes Phys. 874 (Springer, Dordrecht, 2013).CrossRefGoogle Scholar
  13. 13.
    M. A. Baranov, A. V. Chubukov, and M. Yu. Kagan, Int. J. Mod. Phys. B 6, 2471 (1992).ADSCrossRefGoogle Scholar
  14. 14.
    M. Yu. Kagan and A. V. Chubukov, JETP Lett. 47, 525 (1988).Google Scholar
  15. 15.
    A. V. Chubukov and M. Yu. Kagan, J. Phys.: Condens. Matter 1, 3135 (1989).ADSGoogle Scholar
  16. 16.
    M. Yu. Kagan and A. V. Chubukov, JETP Lett. 50, 483 (1989).Google Scholar
  17. 17.
    M. Yu. Kagan, Phys. Lett. A 152, 303 (1991).ADSCrossRefGoogle Scholar
  18. 18.
    M. A. Baranov, D. V. Efremov, and M. Yu. Kagan, Phys. C (Amsterdam, Neth.) 218, 75 (1993).ADSCrossRefGoogle Scholar
  19. 19.
    M. A. Baranov, M. Yu. Kagan, and Yu. Kagan, JETP Lett. 64, 301 (1996).ADSCrossRefGoogle Scholar
  20. 20.
    I. E. Dzyaloshinskii and V. M. Yakovenko, Sov. Phys. JETP 94, 344 (1988).Google Scholar
  21. 21.
    A. I. Kozlov, Supercond.: Phys. Chem. Eng. 2, 64 (1989).Google Scholar
  22. 22.
    K. I. Hur and T. M. Rice, Ann. Phys. 325, 1452 (2009).ADSCrossRefGoogle Scholar
  23. 23.
    V. J. Emery, S. A. Kivelson, and H. Q. Lin, Phys. Rev. Lett. 64, 475 (1990).ADSCrossRefGoogle Scholar
  24. 24.
    M. Yu. Kagan and T. M. Rice, J. Phys.: Condens. Matter 6, 3771 (1994).ADSGoogle Scholar
  25. 25.
    M. Yu. Kagan, R. Fresard, M. Capezzali, and H. Beck, Phys. Rev. B 57, 5995 (1998).ADSCrossRefGoogle Scholar
  26. 26.
    M. Yu. Kagan, R. Fresard, M. Capezzali, and H. Beck, Physica B 284–288, 347 (2000).Google Scholar
  27. 27.
    P. Nozieres and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985).ADSCrossRefGoogle Scholar
  28. 28.
    A. J. Leggett, J. Phys. (Paris) Colloq. 41, C7 (1980).CrossRefGoogle Scholar
  29. 29.
    A. J. Leggett, in Lecture Notes of the 16th Karpacz Winter School of Theoretical Physics, Modern Trends in the Theory of Condensed Matter, Ed. by A. Pekalski and J. Przystawa (Springer, Berlin, 1980), p. 13.Google Scholar
  30. 30.
    R. Combescot, X. Leyronas, and M. Yu. Kagan, Phys. Rev. A 73, 023618 (2006).ADSCrossRefGoogle Scholar
  31. 31.
    H. Feshbach, Ann. Phys. 5, 357 (1958).ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    H. Feshbach, Ann. Phys. 19, 287 (1962).ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    U. Fano, Nuovo Cimento 12, 156 (1935).Google Scholar
  34. 34.
    U. Fano, Phys. Rev. 124, 1866 (1961).ADSCrossRefGoogle Scholar
  35. 35.
    C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, Nature 424, 47 (2003).ADSCrossRefGoogle Scholar
  36. 36.
    C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. 92, 040403 (2004).ADSCrossRefGoogle Scholar
  37. 37.
    M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 91, 250401 (2003).ADSCrossRefGoogle Scholar
  38. 38.
    M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, Phys. Rev. Lett. 92, 120403 (2004).ADSCrossRefGoogle Scholar
  39. 39.
    V. Gurarie and L. Radzihovsky, Ann. Phys. (Weinheim) 322, 2 (2007).ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    J. Ranninger, R. Micnas, and S. Robaszkiewicz, Ann. Phys. 13, 455 (1988).CrossRefGoogle Scholar
  41. 41.
    R. Micnas, J. Ranninger, and S. Robaszkiewicz, Rev. Mod. Phys. 62, 113 (1990).ADSCrossRefGoogle Scholar
  42. 42.
    V. B. Geshkenbein, L. B. Ioffe, and A. I. Larkin, Phys. Rev. B 55, 3173 (1997).ADSCrossRefGoogle Scholar
  43. 43.
    M. Yu. Kagan, I. V. Brodsky, D. V. Efremov, and A. V. Klaptsov, Phys. Rev. A 70, 023607 (2004).ADSCrossRefGoogle Scholar
  44. 44.
    M. Yu. Kagan, A. P. Menushenkov, A. V. Kuznetsov, and K. V. Klementev, Sov. Phys. JETP 93, 615 (2001).ADSCrossRefGoogle Scholar
  45. 45.
    A. P. Menushenkov, A. V. Kuznetsov, K. V. Klementev, and M. Yu. Kagan, J. Supercond. Nov. Magn. 29, 701 (2016).CrossRefGoogle Scholar
  46. 46.
    J. Barden, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    N. N. Bogoliubov, Sov. Phys. JETP 34, 58 (1958).Google Scholar
  48. 48.
    N. N. Bogoliubov, Sov. Phys. JETP 34, 73 (1958).Google Scholar
  49. 49.
    L. P. Gor’kov, Developing BCS ideas in the former Soviet Union, in BCS: 50 Years, Ed. by L. N. Cooper and D. Feldman (World Scientific, Singapore, 2011), p. 107.Google Scholar
  50. 50.
    L. P. Gor’kov, Int. J. Mod. Phys. B 24, 3835 (2010).CrossRefGoogle Scholar
  51. 51.
    A. B. Migdal, Sov. Phys. JETP 34, 958 (1958).MathSciNetGoogle Scholar
  52. 52.
    G. M. Eliashberg, Sov. Phys. JETP 11, 3 (1960).Google Scholar
  53. 53.
    W. L. Mcmilan, Phys. Rev. B 167, 331 (1968).ADSCrossRefGoogle Scholar
  54. 54.
    R. C. Dynes, Solid State Commun. 10, 615 (1972).ADSCrossRefGoogle Scholar
  55. 55.
    P. B. Allen and R. C. Dynes, Phys. Rev. B 12, 905 (1975).ADSCrossRefGoogle Scholar
  56. 56.
    R. Combescot, Phys. Rev. Lett. 67, 148 (1991).ADSCrossRefGoogle Scholar
  57. 57.
    E. Wigner and H. B. Huntington, J. Chem. Phys. 3, 764 (1935).ADSCrossRefGoogle Scholar
  58. 58.
    R. Kronig, J. de Boer, and J. Korringa, Physica (Utrecht) 12, 245 (1946).ADSCrossRefGoogle Scholar
  59. 59.
    A. A. Abrikosov, Astron. Zh. 31, 112 (1954).Google Scholar
  60. 60.
    A. A. Abrikosov, Sov. Phys. JETP 12, 1254 (1961).Google Scholar
  61. 61.
    N. W. Aschkroft, Phys. Rev. Lett. 21, 1748 (1968).ADSCrossRefGoogle Scholar
  62. 62.
    N. W. Aschkroft, Phys. Rev. Lett. 92, 187002 (2004).ADSCrossRefGoogle Scholar
  63. 63.
    E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 34, 1300 (1972).ADSGoogle Scholar
  64. 64.
    E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 35, 783 (1972).ADSGoogle Scholar
  65. 65.
    P. Cudazzo, G. Profeta, A. Sanna, A. Floris, A. Continenza, S. Massidda, and E. K. U. Gross, Phys. Rev. B 81, 134506 (2010).ADSCrossRefGoogle Scholar
  66. 66.
    N. Bernstein, C. Hellberg, M. Johannes, I. Mazin, and M. J. Mehl, Phys. Rev. B 91, 060511(R) (2015).Google Scholar
  67. 67.
    I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J.Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, and F. Mauri, Phys. Rev. Lett. 114, 157004 (2015).ADSCrossRefGoogle Scholar
  68. 68.
    M. I. Eremets, I. A. Trojan, S. A. Medvedev, J. S. Tse, and Y. Yao, Science 319, 1506 (2008).ADSCrossRefGoogle Scholar
  69. 69.
    A. Bianconi and T. Jarlborg, Europhys. Lett. 112, 37001 (2015).ADSCrossRefGoogle Scholar
  70. 70.
    A. Bianconi and T. Jarlborg, Nov. Supercond. Mater. 1, 37 (2015).Google Scholar
  71. 71.
    T. Jarlborg and A. Bianconi, Sci. Rep. 6, 24816 (2016).ADSCrossRefGoogle Scholar
  72. 72.
    W. Kohn, Phys. Rev. Lett. 2, 393 (1959).ADSCrossRefGoogle Scholar
  73. 73.
    J. Friedel, Adv. Phys. 3, 446 (1954).ADSCrossRefGoogle Scholar
  74. 74.
    J. Friedel, Nuovo Cimento Suppl. 7, 287 (1958).CrossRefGoogle Scholar
  75. 75.
    V. M. Galitskii, Sov. Phys. JETP 7, 104 (1958).MathSciNetGoogle Scholar
  76. 76.
    A. V. Chubukov, Phys. Rev. B 48, 1097 (1993).ADSCrossRefGoogle Scholar
  77. 77.
    D. V. Efremov, M. S. Mar’enko, M. A. Baranov, and M. Yu. Kagan, Physica B 284–288, 216 (2000).CrossRefGoogle Scholar
  78. 78.
    M. A. Baranov, D. V. Efremov, M. S. Mar’enko, and M. Yu. Kagan, Sov. Phys. JETP 90, 861 (2000).ADSCrossRefGoogle Scholar
  79. 79.
    P. Bloom, Phys. Rev. B 12, 125 (1975).ADSCrossRefGoogle Scholar
  80. 80.
    M. A. Baranov and M. Yu. Kagan, Zeitschr. Phys. B: Condens. Matter 86, 237 (1992).ADSGoogle Scholar
  81. 81.
    M. A. Baranov and M. Yu. Kagan, Sov. Phys. JETP 99, 1236 (1991).Google Scholar
  82. 82.
    J. Kanamori, Progr. Theor. Phys. 30, 275 (1963).ADSCrossRefGoogle Scholar
  83. 83.
    H. Fukuyama, Y. Hasegawa, and O. Narikiyo, J. Phys. Soc. Jpn. 60, 2013 (1991).ADSCrossRefGoogle Scholar
  84. 84.
    M. Yu. Kagan, D. V. Efremov, M. S. Mar’enko, and V. V. Val’kov, JETP Lett. 93, 819 (2011).CrossRefGoogle Scholar
  85. 85.
    M. Yu. Kagan, V. V. Val’kov, M. M. Korovushkin, and V. A. Mitskan, JETP Lett. 97, 236 (2013).ADSCrossRefGoogle Scholar
  86. 86.
    M. Yu. Kagan, V. V. Val’kov, V. A. Mitskan, and M. M. Korovushkin, Sov. Phys. JETP 117, 728 (2013).ADSCrossRefGoogle Scholar
  87. 87.
    M. Yu. Kagan, V. V. Val’kov, V. A. Mitskan, and M. M. Korovushkin, Sov. Phys. JETP 118, 995 (2014).ADSCrossRefGoogle Scholar
  88. 88.
    M. Yu. Kagan, V. V. Val’kov, V. A. Mitskan, and M. M. Korovushkin, Solid State Commun. 188, 61 (2014).ADSCrossRefGoogle Scholar
  89. 89.
    M. Yu. Kagan, V. A. Mitskan, and M. M. Korovushkin, Eur. Phys. J. B 88, 157 (2015).ADSCrossRefGoogle Scholar
  90. 90.
    M. Yu. Kagan, V. A. Mitskan, and M. M. Korovushkin, J. Exp. Theor. Phys. 119, 1140 (2014).ADSCrossRefGoogle Scholar
  91. 91.
    M. Yu. Kagan, V. A. Mitskan, and M. M. Korovushkin, J. Supercond. Nov. Magn. 29, 1043 (2016).CrossRefGoogle Scholar
  92. 92.
    M. Yu. Kagan, V. A. Mitskan, and M. M. Korovushkin, J. Low Temp. Phys. 1, publ. online Dec. 29, 2015.Google Scholar
  93. 93.
    M. Yu. Kagan, Phys. Usp. 37, 69 (1994).ADSCrossRefGoogle Scholar
  94. 94.
    M. A. Baranov and M. Yu. Kagan, Sov. Phys. JETP 75, 165 (1992).Google Scholar
  95. 95.
    M. Yu. Kagan and V. V. Val’kov, Low Temp. Phys. 37, 84 (2011).Google Scholar
  96. 96.
    M. Yu. Kagan and V. V. Val’kov, in A Lifetime in Magnetism and Superconductivity: A Tribute to Professor David Shoenberg (Cambridge Scientific, Cambridge, 2012), p. 84.Google Scholar
  97. 97.
    M. Yu. Kagan and V. V. Val’kov, J. Exp. Theor. Phys. 113, 156 (2011).ADSCrossRefGoogle Scholar
  98. 98.
    W. Ong, C.-Y. Cheng, I. Arakelyan, and J. E. Thomas, Phys. Rev. Lett. 114, 110403 (2015).ADSCrossRefGoogle Scholar
  99. 99.
    G. Frossati, K. S. Bedell, S. A. J. Wiegers, and G. A. Vermeulen, Phys. Rev. Lett. 57, 1032 (1986).ADSCrossRefGoogle Scholar
  100. 100.
    G. Frossati, S. A. J. Wiegers, T. Tata, R. Jochemsen, P. G. van de Haar, and L. P. Roobol, Czech. J. Phys. 40, 909 (1990).ADSCrossRefGoogle Scholar
  101. 101.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Butterworth-Heinemann, Oxford, 1980).Google Scholar
  102. 102.
    A. Einstein, Sber. Preuss. Akad. Wiss. 1, 3 (1925).Google Scholar
  103. 103.
    V. A. Kashurnikov, N. V. Prokof’ev, and B. V. Svistunov, Phys. Rev. Lett. 87, 120402 (2001).ADSCrossRefGoogle Scholar
  104. 104.
    D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys. Rev. A 71, 012708 (2005).ADSCrossRefGoogle Scholar
  105. 105.
    I. V. Brodsky, M. Yu. Kagan, A. V. Klaptsov, R. Combescot, and X. Leyronas, JETP Lett. 83, 306 (2006).Google Scholar
  106. 106.
    I. V. Brodsky, M. Yu. Kagan, A. V. Klaptsov, R. Combescot, and X. Leyronas, Phys. Rev. A 73, 032724 (2006).ADSCrossRefGoogle Scholar
  107. 107.
    M. Yu. Kagan, I. V. Brodsky, A. V. Klaptsov, R. Combescot, and X. Leyronas, Phys. Usp. 176, 1105 (2006).Google Scholar
  108. 108.
    L. P. Gor’kov and T. K. Melik-Barkhudarov, Sov. Phys. JETP 40, 1452 (1961).Google Scholar
  109. 109.
    D. S. Fisher and P. C. Hohenberg, Phys. Rev. B 37, 4936 (1988).ADSCrossRefGoogle Scholar
  110. 110.
    D. S. Petrov, M. A. Baranov, and G. V. Shlyapnikov, Phys. Rev. A 67, 031601 (2003).ADSCrossRefGoogle Scholar
  111. 111.
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C: Solid State Phys. 6, 1181 (1973).ADSCrossRefGoogle Scholar
  112. 112.
    V. L. Berezinskii, JETP Lett. 34, 610 (1972).Google Scholar
  113. 113.
    K. Miyake, Progr. Theor. Phys. 69, 1794 (1983).ADSCrossRefGoogle Scholar
  114. 114.
    D. V. Efremov and M. Yu. Kagan, Physica B 329–333, 30 (2003).CrossRefGoogle Scholar
  115. 115.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relyativistic Theory (Nauka, Moscow, 1989; Pergamon, Oxford, 1977).Google Scholar
  116. 116.
    M. Randeria, J. M. Duan, and L. Y. Shieh, Phys. Rev. Lett. 62, 981 (1989).ADSCrossRefGoogle Scholar
  117. 117.
    S. Schmitt-Rink, C. M. Varma, and A. E. Ruckenstein, Phys. Rev. Lett. 63, 445 (1989).ADSCrossRefGoogle Scholar
  118. 118.
    M. R. Beasley, J. E. Mooij, and T. P. Orlando, Phys. Rev. Lett. 42, 165 (1979).ADSCrossRefGoogle Scholar
  119. 119.
    A. S. Alexandrov and J. Ranninger, Phys. Rev. B 23, 1796 (1981).ADSCrossRefGoogle Scholar
  120. 120.
    A. S. Alexandrov and J. Ranninger, Phys. Rev. B 24, 1164 (1981).ADSCrossRefGoogle Scholar
  121. 121.
    A. S. Alexandrov, D. A. Samarchenko, and S. V. Traven, Sov. Phys. JETP 66, 567 (1987).Google Scholar
  122. 122.
    A. S. Alexandrov, Phys. Rev. B 38, 925 (1988).ADSCrossRefGoogle Scholar
  123. 123.
    A. S. Alexandrov, Phys. C (Amsterdam, Nether.) 158, 337 (1989).ADSCrossRefGoogle Scholar
  124. 124.
    O. K. Andersen, A. I. Liechtenstein, O. Rodriguez, I. I. Mazin, O. Jepsen, V. P. Antropov, O. Gunnarsson, and S. Gopalan, Phys. C (Amsterdam, Nether.) 185–189, 147 (1991).CrossRefGoogle Scholar
  125. 125.
    E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, Nature 417, 529 (2002).ADSCrossRefGoogle Scholar
  126. 126.
    S. J. J. M. F. Kokkelmans and M. J. Holland, Phys. Rev. Lett. 89, 180401 (2002).ADSCrossRefGoogle Scholar
  127. 127.
    C. M. Varma, Phys. Rev. Lett. 61, 2713 (1988).ADSCrossRefGoogle Scholar
  128. 128.
    A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 124, 1243 (1961).Google Scholar
  129. 129.
    A. I. Larkin, Sov. Phys. JETP 31, 784 (1970).ADSGoogle Scholar
  130. 130.
    A. I. Posazhennikova and M. V. Sadovskii, JETP Lett. 63, 358 (1996).ADSCrossRefGoogle Scholar
  131. 131.
    A. V. Balatsky, I. Vechter, and J. X. Zhu, Rev. Mod. Phys. 78, 373 (2000).ADSCrossRefGoogle Scholar
  132. 132.
    M. V. Feigel’man, L. B. Ioffe, V. E. Kravtsov, and E. Cuevas, Ann. Phys. 325, 1390 (2010).ADSCrossRefGoogle Scholar
  133. 133.
    I. S. Burmistrov, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. 108, 017002 (2012).ADSCrossRefGoogle Scholar
  134. 134.
    M. A. Skvortsov and M. V. Feigel’man, Sov. Phys. JETP 117, 487 (2013).ADSCrossRefGoogle Scholar
  135. 135.
    A. Ghosal, M. Randeria, and N. Triverdi, Phys. Rev. B 65, 014501 (2001).ADSCrossRefGoogle Scholar
  136. 136.
    J. Baringhaus, M. Ruan, F. Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.-P. Li, Z. Jiang, E. H. Conrad, C. Berger, C. Tegenkamp, and W. A. de Heer, Nature Lett. 506, 349 (2014).ADSCrossRefGoogle Scholar
  137. 137.
    P. Esquinazi, T. T. Heikkilä, Y. V. Lysogorskiy, D. A. Tayurskii, and G. E. Volovik, JETP Lett. 100, 336 (2014).ADSCrossRefGoogle Scholar
  138. 138.
    P. G. de Gennes, Superconductivity in Metals and Alloys (Benjamin, New York, 1966).zbMATHGoogle Scholar
  139. 139.
    M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Phys. Rev. Lett. 64, 587 (1990).ADSCrossRefGoogle Scholar
  140. 140.
    A. M. Goldman and N. Markovic, Phys. Today 51, 39 (1998).CrossRefGoogle Scholar
  141. 141.
    D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989).ADSCrossRefGoogle Scholar
  142. 142.
    N. M. Plakida, V. L. Aksenov, and S. L. Drechsler, Europhys. Lett. 4, 1309 (1987).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  1. 1.Kapitza Institute for Physical ProblemsRussian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations