RSS feeds
РусскийEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2015

 / 

August

←  →

Reviews of topical problems


Anomalous superconductivity and superfluidity in repulsive fermion systems

 a, b,  c, d,  c
a HSE University, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation
b Kapitza Institute of Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 117334, Russian Federation
c Kirensky Institute of Physics, Federal Research Center Krasnoyarsk Science Center of the Siberian Branch of the Russian Academy of Sciences, Academgorodok 50, str. 38, Krasnoyarsk, 660036, Russian Federation
d Reshetnev Siberian State Aerospace University, prosp. Gazety Krasnoyarskii rabochii 31, Krasnoyarsk, 660014, Russian Federation

In review, we discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low density. We construct phase diagrams of these systems and find the areas of superconducting state in free space, as well as in the lattice in the framework of the Fermi-gas model with hard-core repulsion, Hubbard model, Shubin—Vonsovsky model, and t—J model. We demonstrate that the critical superconducting temperature can be strongly increased in a spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn—Luttinger mechanism or its generalizations and explains or predicts anomalous p-, d- and f-wave pairing in various materials, such as high-temperature superconductors, idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid 3He, spin-polarized solutions 3He in 4He, ultracold quantum gases in magnetic traps and in the optical lattices.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.3367/UFNe.0185.201508a.0785
Keywords: anomalous superconductivity, Kohn—Luttinger mechanism, superfluidity, repulsive Fermi gas, Hubbard and t—J model, Shubin—Vonsovsky model, graphene monolayer, graphene bilayer
PACS: 67.85.−d, 74.20.−z, 74.20.Mn, 74.20.Rp, 74.25.Dw, 74.78.Fk, 81.05.ue (all)
DOI: 10.3367/UFNe.0185.201508a.0785
URL: https://ufn.ru/en/articles/2015/8/a/
000364717300001
2-s2.0-84947767252
2015PhyU...58..733K
Citation: Kagan M Yu, Mitskan V A, Korovushkin M M "Anomalous superconductivity and superfluidity in repulsive fermion systems" Phys. Usp. 58 733–761 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 15th, May 2015, 9th, June 2015

Оригинал: Каган М Ю, Мицкан В А, Коровушкин М М «Аномальная сверхпроводимость и сверхтекучесть в фермионных системах с отталкиванием» УФН 185 785–815 (2015); DOI: 10.3367/UFNr.0185.201508a.0785

References (311) ↓ Cited by (25) Similar articles (20)

  1. Duan D et al. Sci. Rep. 4 6968 (2014)
  2. Drozdov A P, EremetsMI, Troyan I A arXiv:1412.0460
  3. Bardeen J, Cooper L N, Schrieffer J R Phys. Rev. 108 1175 (1957)
  4. Anderson P W Science 235 1196 (1987)
  5. Regal C A et al. Phys. Rev. Lett. 90 053201 (2003)
  6. Schunck C H et al. Phys. Rev. A 71 045601 (2005)
  7. Ott H R et al. Phys. Rev. Lett. 52 1915 (1984)
  8. Kromer S et al. Phys. Rev. Lett. 81 4476 (1998)
  9. Kuroki K J. Phys. Soc. Jpn. 75 051013 (2006)
  10. Maeno Y, Rice T M, Sigrist M Phys. Today 54 (1) 42 (2001)
  11. Rice T M, Sigrist M J. Phys. Condens. Matter 7 L643 (1995)
  12. Murase et al. Surf. Sci. 170 486 (1986)
  13. Nagamatsu J et al. Nature 410 63 (2001)
  14. Kamihara Y et al. J. Am. Chem. Soc. 130 3296 (2008)
  15. Liu Y et al. arXiv:1503.08587
  16. Vollhardt D, Wölfle P The Superfluid Phases Of Helium 3 (London: Taylor and Francis, 1990)
  17. Volovik G E Exotic Properties Of Superfluid 3He (Singapore: World Scientific, 1992)
  18. Volovik G E The Universe In A Helium Droplet (Oxford: Clarendon Press, 2003)
  19. Novoselov K S et al. Science 306 666 (2004)
  20. Kagan M Yu Usp. Fiz. Nauk 164 77 (1994); Kagan M Yu Phys. Usp. 37 69 (1994)
  21. Ong W et al. Phys. Rev. Lett. 114 110403 (2015)
  22. Ries M G et al. Phys. Rev. Lett. 114 230401 (2015); Ries M G et al. arXiv:1409.5373
  23. Lozovik Yu E, Merkulova S P, Sokolik A A Usp. Fiz. Nauk 178 757 (2008); Lozovik Yu E, Merkulova S P, Sokolik A A Phys. Usp. 51 727 (2008)
  24. Kotov V N et al. Rev. Mod. Phys. 84 1067 (2012)
  25. Wallace P R Phys. Rev. 71 622 (1947)
  26. Castro Neto A H et al. Rev. Mod. Phys. 81 109 (2009)
  27. Kohn W, Luttinger J M Phys. Rev. Lett. 15 524 (1965)
  28. Miyake K J. Phys. Condens. Matter 19 125201 (2007)
  29. Gor’kov L P, Melik-Barkhudarov T K Zh. Eksp. Teor. Fiz. 40 1452 (1961); Gor’kov L P, Melik-Barchudarov T K Sov. Phys. JETP 13 1018 (1961)
  30. Friedel J Adv. Phys. 3 446 (1954)
  31. Friedel J Nuovo Cimento Suppl. 7 287 (1958)
  32. Kagan M Yu i dr. Zh. Eksp. Teor. Fiz. 145 1127 (2014); Kagan M Yu et al. JETP 118 995 (2014)
  33. Kagan M Yu et al. Solid State Commun. 188 61 (2014)
  34. Lindhard J Kongelige Dan. Vidensk. Selsk. Mat. Fys. Medd. 28 8 (1954)
  35. Ashcroft N, Mermin N Solid State Physics Vol. 1 (New York: Rinehart and Winston, 1976); Ashkroft N, Mermin N Fizika Tverdogo Tela Vol. 1 (M.: Mir, 1979)
  36. Migdal A B Zh. Eksp. Teor. Fiz. 34 1438 (1958); Migdal A B Sov. Phys. JETP 7 996 (1958)
  37. Kohn W Phys. Rev. Lett. 2 393 (1959)
  38. Fay D, Layzer A Phys. Rev. Lett. 20 187 (1968)
  39. Kagan M Yu, Chubukov A V Pis’ma ZhETF 47 525 (1988); Kagan M Yu, Chubukov A V JETP Lett. 47 614 (1988)
  40. Baranov M A, Chubukov A V, Kagan M Yu Int. J. Mod. Phys. B 6 2471 (1992)
  41. Baranov M A, Kagan M Yu, Kagan Yu Pis’ma ZhETF 64 273 (1996); Baranov M A, Kagan M Yu, Kagan Yu JETP Lett. 64 301 (1996)
  42. Galitskii V M Zh. Eksp. Teor. Fiz. 34 151 (1958); Galitskii V M Sov. Phys. JETP 7 104 (1958)
  43. Kagan M Yu, Chubukov A V Pis’ma ZhETF 50 483 (1989); Kagan M Yu, Chubukov A V JETP Lett. 50 517 (1989)
  44. Chubukov A V Phys. Rev. B 48 1097 (1993)
  45. Efremov D V et al. Physica B 284 - 288 216 (2000)
  46. Bloom P Phys. Rev. B 12 125 (1975)
  47. Afanas’ev A M, Kagan Yu Zh. Eksp. Teor. Fiz. 43 1456 (1962); Afanas’ev A M, Kagan Yu Sov. Phys. JETP 16 1030 (1962)
  48. Efremov D V i dr. Zh. Eksp. Teor. Fiz. 117 990 (2000); Efremov D V et al. JETP 90 861 (2000)
  49. Oh G-H et al. J. Low Temp. Phys. 95 525 (1994)
  50. Bednorz J G, Müller K A Z. Phys. B 64 189 (1986)
  51. Hubbard J C Proc. R. Soc. Lond. A 276 238 (1963)
  52. Izyumov Yu A, Katsnel’son M I, Skryabin Yu N Magnetizm Kollektivizirovannykh Elektronov (M.: Fizmatlit, 1994)
  53. Izyumov Yu A Usp. Fiz. Nauk 165 403 (1995); Izyumov Yu A Phys. Usp. 38 385 (1995)
  54. Georges A et al. Rev. Mod. Phys. 68 13 (1996)
  55. Tasaki H J. Phys. Condens. Matter 68 4353 (1998)
  56. Val’kov V V, Ovchinnikov S G Kvazichastitsy v Sil’no Korrelirovannykh Sistemakh (Novosibirsk: Izd-vo SO RAN, 2001); Ovchinnikov S G, Val’kov V V Hubbard Operators In The Theory Of Strongly Correlated Electrons (London: Imperial College Press, 2004)
  57. Baranov M A, Kagan M Yu Z. Phys. B 86 237 (1992)
  58. Baranov M A, Kagan M Yu Zh. Eksp. Teor. Fiz. 99 1236 (1991); Baranov M A, Kagan M Yu Sov. Phys. JETP 72 689 (1991)
  59. Scalapino D J, Loh E (Jr.), Hirsch J E Phys. Rev. B 34 8190 (1986)
  60. Scalapino D J, Loh E (Jr.), Hirsch J E Phys. Rev. B 35 6694 (1987)
  61. Kozlov A N Sverkhprovodimost’ 2 64 (1989)
  62. Dzyaloshinskii I E, Krichever I M, Khronek Ya Zh. Eksp. Teor. Fiz. 94 344 (1988); Dzyaloshinskii I E, Krichever I M, Chronek J Sov. Phys. JETP 67 1492 (1988)
  63. Hlubina R Phys. Rev. B 59 9600 (1999)
  64. Zanchi D, Schulz H J Phys. Rev. B 54 9509 (1996)
  65. Dzyaloshinskii I E, Yakovenko V M Zh. Eksp. Teor. Fiz. 94 344 (1988); Dzyaloshinskii I E, Yakovenko V M Sov. Phys. JETP 67 844 (1988)
  66. Zheleznyak A T, Yakovenko V M, Dzyaloshinskii I E Phys. Rev. B 55 3200 (1997)
  67. Raghu S, Kivelson S A, Scalapino D J Phys. Rev. B 81 224505 (2010)
  68. Kagan M Yu Phys. Lett. A 152 303 (1991)
  69. Kagan M Yu, Val’kov V V Zh. Eksp. Teor. Fiz. 140 179 (2011); Kagan M Yu, Val’kov V V JETP 113 156 (2011)
  70. Kagan M Yu, Val’kov V V A Lifetime In Magnetism And Superconductivity: A Tribute To Professor David Schoenberg (Cambridge: Cambridge Sci. Publ., 2011)
  71. Falicov L M, Kimball J C Phys. Rev. Lett. 22 997 (1969)
  72. Kagan Yu, Prokof’ev N V Zh. Eksp. Teor. Fiz. 90 2176 (1986); Kagan Yu, Prokof’ev N V Sov. Phys. JETP 63 1276 (1986)
  73. Kagan Yu, Prokof’ev N V Zh. Eksp. Teor. Fiz. 93 366 (1986); Kagan Yu, Prokof’ev N V Sov. Phys. JETP 66 211 (1987)
  74. Suhl H, Matthias T B, Walker L R Phys. Rev. Lett. 3 552 (1959)
  75. Geilikman B T Zh. Eksp. Teor. Fiz. 48 1194 (1965); Geilikman B T Sov. Phys. JETP 21 796 (1965)
  76. Geilikman B T Usp. Fiz. Nauk 88 327 (1966); Geilikman B T Sov. Phys. Usp. 9 142 (1966)
  77. Geilikman B T Usp. Fiz. Nauk 109 65 (1973); Geilikman B T Sov. Phys. Usp. 16 17 (1973)
  78. Baranov M A, Kagan M Yu Zh. Eksp. Teor. Fiz. 102 313 (1992); Baranov M A, Kagan M Yu JETP 75 165 (1992)
  79. Baranov M A, Efremov D V, Kagan M Yu Physica C 218 75 (1993)
  80. Frossati G et al. Czech. J. Phys. 440 909 (1990)
  81. Wiegers S A J et al. Physica B 165 - 166 733 (1990)
  82. Bedell K S, Sanchez-Castro C Phys. Rev. Lett. 57 854 (1986)
  83. Frossati G et al. Phys. Rev. Lett. 57 1032 (1986)
  84. Dy K S, Pethick C J Phys. Rev. 185 373 (1969)
  85. Bashkin E P, Meyerovich A E Adv. Phys. 30 1 (1981)
  86. Østgaard E, Bashkin E P Physica B 178 134 (1992)
  87. Andreev A F Zh. Eksp. Teor. Fiz. 50 1415 (1966); Andreev A F Sov. Phys. JETP 23 939 (1966)
  88. Zinov’eva K N, Boldarev S T Zh. Eksp. Teor. Fiz. 56 1089 (1969); Zinov’eva K N, Boldarev S T Sov. Phys. JETP 29 585 (1969)
  89. Alikacem N, Sprague D T, Hallock R B Phys. Rev. Lett. 67 2501 (1991)
  90. Higley R H, Sprague D T, Hallock R B Phys. Rev. Lett. 63 2570 (1989)
  91. Saunders J, Lusher C P, Cowan B P Phys. Rev. Lett. 64 2523 (1990)
  92. Lusher C P, Cowan B P, Saunders J Phys. Rev. Lett. 67 2497 (1991)
  93. Miyake K Prog. Theor. Phys. 69 1794 (1983)
  94. Randeria M, Duan J-M, Shieh L-Y Phys. Rev. Lett. 62 981 (1989)
  95. Schmitt-Rink S, Varma C M, Ruckenstein A E Phys. Rev. Lett. 63 445 (1989)
  96. Kagan M Yu Modern Trends In Superconductivity And Superfluidity (Lecture Notes in Physics) Vol. 874 (Dordrecht: Springer, 2013)
  97. Stoof H T C et al. Phys. Rev. Lett. 76 10 (1996)
  98. Larkin A I Zh. Eksp. Teor. Fiz. 58 1466 (1970); Larkin A I Sov. Phys. JETP 31 784 (1970)
  99. Abrikosov A A, Gor’kov L P Zh. Eksp. Teor. Fiz. 39 480 (1960); Abrikosov A A, Gor’kov L P Sov. Phys. JETP 12 337 (1961)
  100. Anderson P W Phys. Rev. Lett. 65 2306 (1990)
  101. Varma C M et al. Phys. Rev. Lett. 63 1996 (1989)
  102. Anderson P W Phys. Rev. Lett. 66 3226 (1991)
  103. Engelbrecht J R, Randeria M Phys. Rev. Lett. 65 1032 (1990)
  104. Fukuyama H, Hasegawa Y, Narikiyo O J. Phys. Soc. Jpn. 60 2013 (1991)
  105. Fabrizio M Doctoral Thesis (1992)
  106. Prokofiev N V, in review article, Stamp P J. Physque 3 625 (1993)
  107. Baranov M A, Kagan M Yu, Mar’enko M S Pis’ma ZhETF 58 734 (1993); Baranov M A, Kagan M Yu, Mar’enko M S JETP Lett. 58 709 (1993)
  108. Kagan M Yu, Val’kov V V, Wölfle P Low Temp. Phys. 37 1046 (2011)
  109. Kanamori J Prog. Theor. Phys. 30 275 (1963)
  110. Alexandrov A S, Kabanov V V Phys. Rev. Lett. 106 136403 (2011)
  111. Shubin S P, Vonsovsky S V Proc. R. Soc. Lond. A 145 159 (1934)
  112. Shubin S P, Vonsovsky S V Phys. Z. Sowjetunion. 7 292 (1935)
  113. Shubin S P, Vonsovsky S V Phys. Z. Sowjetunion 10 348 (1936)
  114. Vonsovsky S V, Katsnelson M I J. Phys. C Solid State Phys. 12 2043 (1979)
  115. Vonsovsky S V, Katsnelson M I J. Phys. C Solid State Phys. 12 2055 (1979)
  116. Zaitsev R O Zh. Eksp. Teor. Fiz. 78 1132 (1980); Zaitsev R O Sov. Phys. JETP 51 671 (1980)
  117. Zaitsev R O, Ivanov V A, Mikhailova Yu V Fiz. Met. Metalloved. 65 1032 (1988)
  118. Zaitsev R O, Ivanov V A, Mikhailova Yu V Fiz. Met. Metalloved. 65 1108 (1989)
  119. Val’kov V V, Korovushkin M M Zh. Eksp. Teor. Fiz. 139 126 (2011); Val’kov V V, Korovushkin M M JETP 112 108 (2011)
  120. Kagan M Yu et al. Pis’ma ZhETF 93 807 (2011); Kagan M Yu et al. JETP Lett. 93 725 (2011)
  121. Landau L D, Lifshits E M Kvantovaya Mekhanika: Nerelyativistskaya Teoriya (M.: Nauka, 1989); Landau L D, Lifshitz E M Quantum Mechanics: Non-Relativistic Theory (Oxford: Butterworth-Heinemann, 1991)
  122. Raghu S et al. Phys. Rev. B 85 024516 (2012)
  123. Kagan M Yu i dr. Pis’ma ZhETF 97 253 (2013); Kagan M Yu et al. JETP Lett. 97 226 (2013)
  124. Kagan M Yu i dr. Zh. Eksp. Teor. Fiz. 144 837 (2013); Kagan M Yu et al. JETP 117 728 (2013)
  125. Deng Y et al. Europhys. Lett. 110 57001 (2015); Deng Y et al. arXiv:1408.2088
  126. Okazaki K et al. Science 337 1314 (2012)
  127. Izyumov Yu A Usp. Fiz. Nauk 161 (11) 1 (1991); Izyumov Yu A Sov. Phys. Usp. 34 935 (1991)
  128. Brenig W Phys. Rep. 251 153 (1995)
  129. Izyumov Yu A Usp. Fiz. Nauk 167 465 (1997); Izyumov Yu A Phys. Usp. 40 445 (1997)
  130. Plakida N M Condens. Matter Phys. 5 707 (2002)
  131. Bulaevskii L N, Nagaev E L, Khomskii D I Zh. Eksp. Teor. Fiz. 54 1562 (1968); Bulaevskii L N, Nagaev E L, Khomskii D I Sov. Phys. JETP 27 836 (1968)
  132. Chao K A, Spalek J, Oles A M J. Phys. C Solid State Phys. 10 L271 (1977)
  133. Hybertsen M S, Schluter M, Christensen N E Phys. Rev. B 39 9028 (1989)
  134. Unger P, Fulde P Phys. Rev. B 47 8947 (1993)
  135. Emery V J Phys. Rev. Lett. 58 2794 (1987)
  136. Varma C M, Schmitt-Rink S, Abrahams E Solid State Commun. 62 681 (1987)
  137. Kagan M Yu, Rice T M J. Phys. Condens. Matter 6 3771 (1994)
  138. Plakida N M Pis’ma ZhETF 74 38 (2001); Plakida N M JETP Lett. 74 36 (2001)
  139. Plakida N M i dr. Zh. Eksp. Teor. Fiz. 124 367 (2003); Plakida N M et al. JETP 97 331 (2003)
  140. Hubbard J C Proc. R. Soc. Lond. A 285 542 (1965)
  141. Zhang F C, Rice T M Phys. Rev. B 37 3759 (1988)
  142. Zaitsev R O, Ivanov V A Fiz. Tverd. Tela 29 2554 (1987); Zaitsev R O, Ivanov V A Sov. Phys. Solid State 29 475 (1987)
  143. Zaitsev R O Zh. Eksp. Teor. Fiz. 125 891 (2004); Zaitsev R O JETP 98 780 (2004)
  144. Laughlin R B Phys. Rev. Lett. 60 2677 (1988)
  145. Fetter A L, Hanna C B, Laughlin R B Phys. Rev. B 39 9679 (1989)
  146. Kagan M Yu et al. Phys. Rev. A 70 023607 (2004)
  147. Kagan M Yu i dr. Usp. Fiz. Nauk 176 1105 (2006); Kagan M Yu et al. Phys. Usp. 49 1079 (2006)
  148. Brinkman W F, Rice T M Phys. Rev. B 2 1324 (1970)
  149. Sachdev S Phys. Status Solidi B 247 537 (2010)
  150. Lee J, Strack P, Sachdev S Phys. Rev. B 87 045104 (2013)
  151. Castellani C, Di Castro C, Grilli M Phys. Rev. Lett. 75 4650 (1995)
  152. Zaitsev R O Zh. Eksp. Teor. Fiz. 68 207 (1975); Zaitsev R O Sov. Phys. JETP 41 100 (1975)
  153. Zaitsev R O Zh. Eksp. Teor. Fiz. 70 1100 (1976); Zaitsev R O Sov. Phys. JETP 43 574 (1976)
  154. Eremin M, Eremin I, Varlamov S Phys. Rev. B 64 214512 (2001)
  155. Eremin M V, Shigapov I M, Eremin I M Eur. Phys. J. B 85 131 (2012)
  156. Plakida N M, Oudovenko V S Eur. Phys. J. B 86 115 (2013)
  157. Plakida N M, Oudovenko V S Zh. Eksp. Teor. Fiz. 146 631 (2014); Plakida N M, Oudovenko V S JETP 119 554 (2014)
  158. Hirsch J E Phys. Lett. A 136 153 (1989)
  159. Yushankhai V Yu, Vujicic G M, Zakula R B Phys. Lett. A 151 254 (1990)
  160. Val’kov V V i dr. Pis’ma ZhETF 75 450 (2002); Val’kov V V et al. JETP Lett. 75 378 (2002)
  161. Val’kov V V, Dzebisashvili D M Zh. Eksp. Teor. Fiz. 127 686 (2005); Val’kov V V, Dzebisashvili D M JETP 100 608 (2005)
  162. Korshunov M M, Ovchinnikov S G, Sherman A V Pis’ma ZhETF 80 45 (2004); Korshunov M M, Ovchinnikov S G, Sherman A V JETP Lett. 80 39 (2004)
  163. Val’kov V V, Golovnya A A Zh. Eksp. Teor. Fiz. 134 1167 (2008); Val’kov V V, Golovnya A A JETP 107 996 (2008)
  164. Val’kov V V, Korovushkin M M, Barabanov A F Pis’ma 88 426 (2008); Val’kov V V, Korovushkin M M, Barabanov A F JETP Lett. 88 370 (2008)
  165. Val’kov V V i dr. Fiz. Tverd. Tela 53 1895 (2011); Val’kov V V et al. Phys. Solid State 53 1997 (2011)
  166. Bermudez A, Porras D arXiv:1504.00128
  167. Marienko M S, Sau J D, Tewari S arXiv:1202.5784
  168. Novoselov K S et al. Nature 438 197 (2005)
  169. Tan Y-W et al. Phys. Rev. Lett. 99 246803 (2007)
  170. Morozov S V et al. Phys. Rev. Lett. 100 016602 (2008)
  171. Bolotin K I et al. Solid State Commun. 146 351 (2008)
  172. Garcia N et al. Phys. Rev. B 78 035413 (2008)
  173. Geim A K, Katsnelson M I, Novoselov K S Nature Phys. 2 620 (2006)
  174. Young A F, Kim P Nature Phys. 5 222 (2009)
  175. Katsnelson M I Eur. Phys. J. B 51 157 (2006)
  176. Rusin T M, Zawadzki W Phys. Rev. B 80 045416 (2009)
  177. Nair P R et al. Science 320 1308 (2008)
  178. Muñoz W A, Covaci L, Peeters F M Phys. Rev. B 86 184505 (2012)
  179. Heersche H B et al. Nature 446 56 (2007)
  180. Josephson B D Phys. Lett. 1 251 (1962)
  181. Shailos A et al. Europhys. Lett. 79 57008 (2007)
  182. Titov M, Beenakker C W J Phys. Rev. B 74 041401R (2006)
  183. Du X, Skachko I, Andrei E Y Phys. Rev. B 77 184507 (2008)
  184. Ojeda-Aristizabal C et al. Phys. Rev. B 79 165436 (2009)
  185. Tomori H et al. Physica C 470 1492 (2010)
  186. Peres N M R, Guinea F, Castro Neto A H Phys. Rev. B 72 174406 (2005)
  187. Esquinazi P Physics 5 050007 (2013)
  188. Marino E C, Nunes L H C M Nucl. Phys. B 741 404 (2006)
  189. González J, Guinea F, Vozmediano M A H Phys. Rev. B 63 134421 (2001)
  190. Zhao E, Paramekanti A Phys. Rev. Lett. 97 230404 (2006)
  191. Uchoa B, Castro Neto A H Phys. Rev. Lett. 98 146801 (2007)
  192. Kopnin N B, Sonin E B Phys. Rev. Lett. 100 246808 (2008)
  193. Basko D M, Aleiner I L Phys. Rev. B 77 041409(R) (2008)
  194. Lozovik Yu E, Ogarkov S L, Sokolik A A Phil. Trans. R. Soc. A 368 5417 (2010)
  195. Einenkel M, Efetov K B Phys. Rev. B 84 214508 (2011)
  196. Classen L, Scherer M M, Honerkamp C Phys. Rev. B 90 035122 (2014)
  197. Black-Schaffer A M, Doniach S Phys. Rev. B 75 134512 (2007)
  198. Black-Schaffer A M, Wu W, Le Hur K Phys. Rev. B 90 054521 (2014)
  199. Black-Schaffer A M, Honerkamp C J. Phys. Condens. Matter 26 423201 (2014)
  200. Krishana K et al. Science 277 83 (1997)
  201. Elhalel K et al. Phys. Rev. Lett. 98 137002 (2007)
  202. Balatsky A V Phys. Rev. Lett. 80 1972 (1998)
  203. Volovik G E Phys. Lett. A 128 277 (1988)
  204. Biswas P K et al. Phys. Rev. B 87 180503(R) (2013)
  205. Nishikubo Y, Kudo K, Nohara M J. Phys. Soc. Jpn. 80 055002 (2011)
  206. Honerkamp C Phys. Rev. Lett. 100 146404 (2008)
  207. Daul S, Scalapino D J, White S R Phys. Rev. Lett. 84 4188 (2000)
  208. Ma T et al. Phys. Rev. B 84 121410(R) (2011)
  209. Chen K S et al. Phys. Rev. B 88 041103(R) (2013)
  210. González J Phys. Rev. B 78 205431 (2008)
  211. Markiewicz R S J. Phys. Chem. Solids 58 1179 (1997)
  212. Valenzuela B, Vozmediano M A H New J. Phys. 10 113009 (2008)
  213. McChesney J L et al. Phys. Rev. Lett. 104 136803 (2010)
  214. Gofron K et al. Phys. Rev. Lett. 73 3302 (1994)
  215. Van Hove L Phys. Rev. 89 1189 (1953)
  216. Nandkishore R, Levitov L S, Chubukov A V Nature Phys. 8 158 (2012)
  217. Nandkishore R, Chern G-W, Chubukov A V Phys. Rev. Lett. 108 227204 (2012)
  218. Dzyaloshinskii I E Zh. Eksp. Teor. Fiz. 93 1487 (1987); Dzyaloshinskii I E Sov. Phys. JETP 66 848 (1987)
  219. Schulz H J Europhys. Lett. 4 609 (1987)
  220. Shankar R Rev. Mod. Phys. 66 129 (1994)
  221. Makogon D et al. Phys. Rev. B 84 125404 (2011)
  222. Li T Europhys. Lett. 97 37001 (2012)
  223. Wang W S et al. Phys. Rev. B 85 035414 (2012)
  224. Nandkishore R, Chubukov A V Phys. Rev. B 86 115426 (2012)
  225. Kiesel M L et al. Phys. Rev. B 86 020507(R) (2012)
  226. Wehling T O et al. Phys. Rev. Lett. 106 236805 (2011)
  227. Levin A A Vvedenie v Kvantovuyu Khimiyu Tverdogo Tela (M.: Khimiya, 1974); Levin A A Solid State Quantum Chemistry (New York: McGraw-Hill, 1977)
  228. Reich S et al. Phys. Rev. B 66 035412 (2002)
  229. Perfetto E et al. Phys. Rev. B 76 233408 (2007)
  230. Nandkishore R, Thomale R, Chubukov A V Phys. Rev. B 89 144501 (2014)
  231. Kagan M Yu, Mitskan V A, Korovushkin M M Eur. Phys. J. B 88 157 (2015)
  232. Zaitsev R O Pis’ma ZhETF 94 224 (2011); Zaitsev R O JETP Lett. 94 206 (2011)
  233. Zaitsev R O Pis’ma ZhETF 95 423 (2012); Zaitsev R O JETP Lett. 95 380 (2012)
  234. Guinea F, Castro Neto A H, Peres N M R Phys. Rev. B 73 245426 (2006)
  235. Kagan M Yu, Mitskan V A, Korovushkin M M Zh. Eksp. Teor. Fiz. 146 1301 (2014); Kagan M Yu, Mitskan V A, Korovushkin M M JETP 119 1140 (2014)
  236. McCann E, Fal’ko V I Phys. Rev. Lett. 96 086805 (2006)
  237. Nilsson J et al. Phys. Rev. B 73 214418 (2006)
  238. Partoens B, Peeters F M Phys. Rev. B 74 075404 (2006)
  239. McCann E, Abergel D S L, Fal’ko V I Eur. Phys. J. Special Topics 148 91 (2007)
  240. McCann E, Koshino M Rep. Prog. Phys. 76 056503 (2013)
  241. Nunes L H C M, Mota A L, Marino E C Solid State Commun. 152 2082 (2012)
  242. Vučičević J, Goerbig M O, Milovanović M V Phys. Rev. B 86 214505 (2012)
  243. Milovanović M V, Predin S Phys. Rev. B 86 195113 (2012)
  244. Hosseini M V, Zareyan M Phys. Rev. Lett. 108 147001 (2012)
  245. Hosseini M V, Zareyan M Phys. Rev. B 86 214503 (2012)
  246. Alford M, Rajagopal K, Wilczek F Nucl. Phys. B 537 443 (1999)
  247. Sedrakian A, Lombardo U Phys. Rev. Lett. 84 602 (2000)
  248. Hwang E H, Das Sarma S Phys. Rev. Lett. 101 156802 (2012)
  249. González J Phys. Rev. B 88 125434 (2013)
  250. Murray J M, Vafek O Phys. Rev. B 89 205119 (2014)
  251. Dresselhaus M S, Dresselhaus G Adv. Phys. 51 1 (2002)
  252. Brandt N B, Chudinov S M, Ponomarev Y G Semimetals (Modern Problems in Condensed Matter Sciences) Vol. 20 (Eds V M Agranovich, A A Maradudin) (Amsterdam: North-Holland, 1988)
  253. Girifalco L A, Hodak M Phys. Rev. B 65 125404 (2002)
  254. Hasegawa M, Nishidate K Phys. Rev. B 70 205431 (2004)
  255. Hasegawa M, Nishidate K, Iyetomi H Phys. Rev. B 76 115424 (2007)
  256. Boström M, Sernelius B E Phys. Rev. A 85 012508 (2012)
  257. Klimchitskaya G L, Mostepanenko V M Phys. Rev. B 87 075439 (2013)
  258. Anderson P W Phys. Rev. Lett. 3 325 (1959)
  259. Tsuneto T Prog. Theor. Phys. 28 857 (1962)
  260. Markowitz D, Kadanoff L P Phys. Rev. 131 563 (1963)
  261. Löthman T, Black-Schaffer A M Phys. Rev. B 90 224504 (2014)
  262. Kats E I, Lebedev V V Phys. Rev. B 89 125433 (2014)
  263. Cardona M Phys. Rev. 140 A651 (1965)
  264. Shanthi N, Sarma D D Phys. Rev. B 57 2153 (1998)
  265. van der Marel D, van Mechelen J L M, Mazin I I Phys. Rev. B 84 205111 (2011)
  266. Schooley J F, Hosler W R, Cohen M L Phys. Rev. Lett. 12 474 (1964)
  267. Koonce C S et al. Phys. Rev. 163 380 (1967)
  268. Binning G et al. Phys. Rev. Lett. 45 1352 (1980)
  269. Reyren N et al. Science 317 1196 (2007)
  270. Heber J Nature 459 28 (2009)
  271. Caviglia A D et al. Nature 456 624 (2008)
  272. Bell C et al. Phys. Rev. Lett. 103 226802 (2009)
  273. Cohen M L Phys. Rev. 134 A511 (1964)
  274. Kahn A H, Leyendecker A J Phys. Rev. 135 A1321 (1964)
  275. Eagles D M Phys. Rev. 164 489 (1967)
  276. Eagles D M Phys. Rev. 186 456 (1969)
  277. Koonce C S, Cohen M L Phys. Rev. 177 707 (1969)
  278. Appel J Phys. Rev. 180 508 (1969)
  279. Zinamon Z Philos. Mag. 21 347 (1970)
  280. Jarlborg T Phys. Rev. B 61 9887 (2000)
  281. Fernandes R M et al. Phys. Rev. B 87 014510 (2013)
  282. Ponomarenko L A et al. Nat. Phys. 7 958 (2011)
  283. Brittnell L et al. Science 335 947 (2012)
  284. Brittnell L et al. Nano Lett. 12 1707 (2012)
  285. Gorbachev R V et al. Nature Phys. 8 896 (2012)
  286. Sakai Y, Koretsune T, Saito S Phys. Rev. B 83 205434 (2011)
  287. Hoffman D M, Doll G L, Eklund P C Phys. Rev. B 30 6051 (1984)
  288. Blase X et al. Phys. Rev. B 51 6868 (1995)
  289. Watanabe K, Taniguchi T, Kanda H Nature Mater. 3 404 (2004)
  290. Kubota Y et al. Science 317 932 (2007)
  291. Lee G-H et al. Appl. Phys. Lett. 99 243114 (2011)
  292. Dean C R et al. Nature Nanotechnol. 5 722 (2010)
  293. Mayorov A S et al. Nano Lett. 11 2396 (2011)
  294. Gannett W et al. Appl. Phys. Lett. 98 242105 (2011)
  295. Xue J et al. Nature Mater. 10 282 (2011)
  296. Decker R et al. Nano Lett. 11 2291 (2011)
  297. Guinea F, Uchoa B Phys. Rev. B 86 134521 (2012)
  298. Lewenstein M et al. Adv. Phys. 56 243 (2007)
  299. Bloch I, Dalibard J, Zwerger W Rev. Mod. Phys. 80 885 (2008)
  300. Zhu S-L, Wang B, Duan L-M Phys. Rev. Lett. 98 260402 (2007)
  301. Wunsch B, Guinea F, Sols F New J. Phys. 10 103027 (2008)
  302. Stamper-Kurn D M et al. Phys. Rev. Lett. 83 2876 (1999)
  303. Anglin J R, Ketterle W Nature 416 211 (2002)
  304. Zwierlein M W et al. Science 311 492 (2006)
  305. Shin Y et al. Phys. Rev. Lett. 97 030401 (2006)
  306. Tarruell L et al. Nature Lett. 483 302 (2012)
  307. Hasegawa Y et al. Phys. Rev. B 74 033413 (2006)
  308. Montambaux G et al. Phys. Rev. B 80 153412 (2009)
  309. Lee K L et al. Phys. Rev. A 80 043411 (2009)
  310. Pereira V M, Castro Neto A H, Peres N M R Phys. Rev. B 80 045401 (2009)
  311. Posazhennikova A I, Sadovskii M V Pis’ma ZhETF 63 347 (1996); Posazhennikova A I, Sadovskii M V JETP Lett. 63 358 (1996)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions