RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2021

 / 

July

←  →

Reviews of topical problems


Spin-polaron concept in the theory of normal and superconducting states of cuprates

†  a, ‡  a, b, §  a, *  c
a 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
b M. F. Reshetnev Siberian State University of Science and Technologies, Krasnoyarsky Rabochy Av. 31, Krasnoyarsk, 660014, Russian Federation
c Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

The review discusses the emergence of the spin-fermion model of cuprates and the formation of the spin-polaron concept of the electronic structure of hole-doped cuprate superconductors. This concept has allowed describing the properties of cuprates in the normal phase as well as the features of superconducting pairing in the unified approach. The derivation of the spin-fermion model from the Emery model in the regime of strong electronic correlations is described, demonstrating the appearance of strong coupling between the spins of copper ions and holes on oxygen ions. Such a strong interaction against the background of the singlet state of the spin subsystem of copper ions (quantum spin liquid) leads to the formation of special Fermi quasiparticles — nonlocal spin polarons. Under doping, the spin-polaron ensemble exhibits instability with respect to superconducting d-wave pairing, whereas superconducting s-wave pairing is not implemented. At the optimal doping, the transition to the superconducting phase occurs at temperatures corresponding to experimental data. It is shown that the superconducting d-wave pairing of spin-polaron quasiparticles is not suppressed by the Coulomb repulsion of holes located on neighboring oxygen ions. It is emphasized that, when the spectral characteristics of spin-polaron quasiparticles are taken into account, the calculated temperature and doping dependences of the London penetration depth are in good agreement with experimental data.

Fulltext pdf (1000 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2020.08.038829
Keywords: strongly correlated electron systems, high-temperature superconductivity, spin polarons, intersite Coulomb interaction, London penetration depth
PACS: 71.10.−w, 71.10.Fd, 71.27.+a, 74.20.−z, 74.20.Mn, 74.25.N−, 74.72.−h (all)
DOI: 10.3367/UFNe.2020.08.038829
URL: https://ufn.ru/en/articles/2021/7/a/
000702491600001
2-s2.0-85116935286
2021PhyU...64..641V
Citation: Val’kov V V, Dzebisashvili D M, Korovushkin M M, Barabanov A F "Spin-polaron concept in the theory of normal and superconducting states of cuprates" Phys. Usp. 64 641–670 (2021)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 22nd, April 2020, revised: 4th, July 2020, 18th, August 2020

Оригинал: Вальков В В, Дзебисашвили Д М, Коровушкин М М, Барабанов А Ф «Спин-поляронная концепция в теории нормального и сверхпроводящего состояний купратов» УФН 191 673–704 (2021); DOI: 10.3367/UFNr.2020.08.038829

References (329) ↓ Cited by (7) Similar articles (20)

  1. Damascelli A, Hussain Z, Shen Z-X Rev. Mod. Phys. 75 473 (2003)
  2. Fischer Ø et al Rev. Mod. Phys. 79 353 (2007)
  3. Fournier D et al Nat. Phys. 6 905 (2010)
  4. Timusk T, Statt B Rep. Prog. Phys. 62 61 (1999)
  5. Chakravarty S et al Phys. Rev. B 63 094503 (2001)
  6. Sadovskii M V Usp. Fiz. Nauk 171 539 (2001); Sadovskii M V Phys. Usp. 44 515 (2001)
  7. Lee P A et al Rev. Mod. Phys. 78 17 (2006)
  8. Yang K-Y, Rice T M, Zhang F-C Phys. Rev. B 73 174501 (2006)
  9. Hussey N E Adv. Phys. 51 1685 (2002)
  10. Riggs S C et al Nat. Phys. 7 332 (2011)
  11. Chang J et al Nat. Phys. 8 871 (2012)
  12. Mamsurova L G i dr Pis’ma ZhETF 105 223 (2017); Mamsurova L G et al JETP Lett. 105 241 (2017)
  13. Mamsurova L G i dr Pis’ma ZhETF 106 351 (2017); Mamsurova L G et al JETP Lett. 106 378 (2017)
  14. Gabovich A M et al Supercond. Sci. Technol. 14 R1 (2001)
  15. Forgan E M et al Nat. Commun. 6 10064 (2015)
  16. Shen K M et al Science 307 901 (2005)
  17. Vojta M Adv. Phys. 58 699 (2009)
  18. Berg E et al New J. Phys. 11 115004 (2009)
  19. Plakida N High-Temperature Cuprate Superconductors: Experiment, Theory, And Applications (Dordrecht: Springer, 2010)
  20. Keimer B et al Nature 518 179 (2015)
  21. Zhang F C, Rice T M Phys. Rev. B 37 3759(R) (1988)
  22. Emery V J Phys. Rev. Lett. 58 2794 (1987)
  23. Anderson P W Science 235 1196 (1987)
  24. Barabanov A F, Maksimov L A, Uimin G V Pis’ma ZhETF 47 532 (1988); Barabanov A F, Maksimov L A, Uimin G V JETP Lett. 47 622 (1988)
  25. Barabanov A F, Maksimov L A, Uimin G V Zh. Eksp. Teor. Fiz. 96 665 (1989); Barabanov A F, Maksimov L A, Uimin G V Sov. Phys. JETP 69 371 (1989)
  26. Prelovšek P Phys. Lett. A 126 287 (1988)
  27. Zaanen J, Oleś A M Phys. Rev. B 37 9423 (1988)
  28. Stechel E B, Jennison D R Phys. Rev. B 38 4632 (1988)
  29. Emery V J, Reiter G Phys. Rev. B 38 4547 (1988)
  30. Matsukawa H, Fukuyama H J. Phys. Soc. Jpn. 58 2845 (1989)
  31. Kuzian R O et al Phys. Rev. B 58 6194 (1998)
  32. Barabanov A F, Maksimov L A, Mikheyenkov A V AIP Conf. Proc. 527 1 (2000)
  33. Barabanov A F, Mikheenkov A V, Belemuk A M Pis’ma ZhETF 75 118 (2002); Barabanov A F, Mikheenkov A V, Belemuk A M JETP Lett. 75 107 (2002)
  34. Maksimov L A, Barabanov A F, Kuzian R O Phys. Lett. A 232 286 (1997)
  35. Maksimov L A, Hayn R, Barabanov A F Phys. Lett. A 238 288 (1998)
  36. Barabanov A F i dr Pis’ma ZhETF 68 386 (1998); Barabanov A F et al JETP Lett. 68 412 (1998)
  37. Barabanov A F et al Phys. Lett. A 265 221 (2000)
  38. Kampf A P, Schrieffer J R Phys. Rev. B 42 7967 (1990)
  39. Barabanov A F i dr Zh. Eksp. Teor. Fiz. 119 777 (2001); Barabanov A F et al J. Exp. Theor. Phys. 92 677 (2001)
  40. Dzebisashvili D M, Val’kov V V, Barabanov A F Pis’ma 98 596 (2013); Dzebisashvili D M, Val’kov V V, Barabanov A F JETP Lett. 98 528 (2013)
  41. 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)
  42. Val’kov V V, Dzebisashvili D M, Barabanov A F Phys. Lett. A 379 421 (2015)
  43. Val’kov V V i dr Pis’ma ZhETF 103 433 (2016); Val’kov V V et al JETP Lett. 103 385 (2016)
  44. Val’kov V V i dr Zh. Eksp. Teor. Fiz. 152 957 (2017); Val’kov V V et al J. Exp. Theor. Phys. 125 810 (2017)
  45. Piekars P, Konior J, Jefferson J H Phys. Rev. B 59 14697 (1999)
  46. Makarov I A et al Phys. Rev. B 92 155143 (2015)
  47. Shneider E I i dr Zh. Eksp. Teor. Fiz. 153 820 (2018); Shneyder E I et al J. Exp. Theor. Phys. 126 683 (2018)
  48. Myasnikova A E, Zhileeva E A, Moseykin D V J. Phys. Condens. Matter 30 125601 (2018)
  49. Myasnikova A E et al J. Phys. Condens. Matter 31 235602 (2019)
  50. Eliashberg G M Zh. Eksp. Teor. Fiz. 38 966 (1960); Eliashberg G M Sov. Phys. JETP 11 696 (1960)
  51. Sadovskii M V Zh. Eksp. Teor. Fiz. 155 527 (2019); Sadovskii M V J. Exp. Theor. Phys. 128 455 (2019)
  52. Dzebisashvili D M, Komarov K K Eur. Phys. J. B 91 278 (2018)
  53. Bardeen J, Cooper L N, Schrieffer J R Phys. Rev. 108 1175 (1957)
  54. Little W A Phys. Rev. 134 A1416 (1964)
  55. Ginzburg V L Phys. Lett. 13 101 (1964)
  56. Bednorz J G, Müller K A Z. Phys. B 64 189 (1986)
  57. Wu M K et al Phys. Rev. Lett. 58 908 (1987)
  58. Schilling A et al Nature 363 56 (1993)
  59. Chu C W et al Nature 365 323 (1993)
  60. Hubbard J C Proc. R. Soc. Lond. A 276 238 (1963)
  61. Ovchinnikov S G Usp. Fiz. Nauk 167 1043 (1997); Ovchinnikov S G Phys. Usp. 40 993 (1997)
  62. Val’kov V V, Ovchinnikov S G Kvazichastitsy v Sil’no Korrelirovannykh Sistemakh (Novosibirsk: Izd-vo SO RAN, 2001); Per. na angl. yaz., Ovchinnikov S G, Val’kov V V Hubbard Operators In The Theory Of Strongly Correlated Electrons (London: Imperial College Press, 2004)
  63. Izyumov Yu A Usp. Fiz. Nauk 167 465 (1997); Izyumov Yu A Phys. Usp. 40 445 (1997)
  64. Loktev V M FNT 22 3 (1996); Loktev V M Low Temp. Phys. 22 1 (1996)
  65. Mott N F Metal - Insulator Transitions (London: Taylor and Francis, 1990); Per. na russk. yaz., Mott N F Perekhody Metall - Izolyator (M.: Nauka, 1979)
  66. Khomskii D I Fiz. Met. Metalloved. 29 31 (1970); Khomskii D I Phys. Met. Metallogr. 29 31 (1970)
  67. Izyumov Yu A Usp. Fiz. Nauk 161 (11) 1 (1991); Izyumov Yu A Sov. Phys. Usp. 34 935 (1991)
  68. Baranov M A, Kagan M Yu Z. Phys. B 86 237 (1992)
  69. Kohn W, Luttinger J M Phys. Rev. Lett. 15 524 (1965)
  70. Fay D, Layzer A Phys. Rev. Lett. 20 187 (1968)
  71. Kagan M Yu, Chubukov A V Pis’ma ZhETF 47 525 (1988); Kagan M Yu, Chubukov A V JETP Lett. 47 614 (1988)
  72. Baranov M A, Chubukov A V, Kagan M Yu Int. J. Mod. Phys. B 6 2471 (1992)
  73. Alexandrov A S, Kabanov V V Phys. Rev. Lett. 106 136403 (2011)
  74. Maiti S, Chubukov A V AIP Conf. Proc. 1550 3 (2013)
  75. Kagan M Yu, Mitskan V A, Korovushkin M M Usp. Fiz. Nauk 185 785 (2015); Kagan M Yu, Mitskan V A, Korovushkin M M Phys. Usp. 58 733 (2015)
  76. Kagan M Yu Pis’ma ZhETF 103 822 (2016); Kagan M Yu JETP Lett. 103 728 (2016)
  77. Scalapino D J, Loh E (Jr.), Hirsch J E Phys. Rev. B 34 8190(R) (1986)
  78. Scalapino D J, Loh E (Jr.), Hirsch J E Phys. Rev. B 35 6694 (1987)
  79. Kozlov A N Sverkhprovodimost’ 2 64 (1989)
  80. Zanchi D, Schulz H J Phys. Rev. B 54 9509 (1996)
  81. Hlubina R Phys. Rev. B 59 9600 (1999)
  82. Raghu S, Kivelson S A, Scalapino D J Phys. Rev. B 81 224505 (2010)
  83. Rømer A T et al Phys. Rev. Res. 2 013108 (2020)
  84. Astretsov G V, Rohringer G, Rubtsov A N Phys. Rev. B 101 075109 (2020)
  85. 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)
  86. Hubbard J C Proc. R. Soc. Lond. A 285 542 (1965)
  87. Shubin S, Vonsowsky S Proc. R. Soc. Lond. A 145 159 (1934)
  88. Shubin S, Vonsowsky S Phys. Z. Sowjetunion 7 292 (1935)
  89. Shubin S, Vonsowsky S Phys. Z. Sowjetunion 10 348 (1936)
  90. Zaitsev R O, Ivanov V A, Mikhailova Yu V Fiz. Met. Metalloved. 65 1032 (1988)
  91. Zaitsev R O, Ivanov V A, Mikhailova Yu V Fiz. Met. Metalloved. 68 1108 (1989)
  92. Zaitsev R O Zh. Eksp. Teor. Fiz. 125 891 (2004); Zaitsev R O J. Exp. Theor. Phys. 98 780 (2004)
  93. Izyumov Yu A, Skryabin Yu N Statisticheskaya Mekhanika Magnitouporyadochennykh Sistem (M.: Nauka, 1987); Per. na angl. yaz., Izyumov Yu A, Skryabin Yu N Statistical Mechanics Of Magnetically Ordered Systems (Berlin: Springer, 1988)
  94. Izyumov Yu A, Katsnel’son M I, Skryabin Yu N Magnetizm Kollektivizirovannykh Elektronov (M.: Nauka, 1994)
  95. Izyumov Yu A, Chashchin N I, Alekseev D S Teoriya Sil’no Korrelirovannykh Sistem. Metod Proizvodyashchego Funktsionala (M. - Izhevsk: RKhD, 2006)
  96. Izyumov Yu A Usp. Fiz. Nauk 165 403 (1995); Izyumov Yu A Phys. Usp. 38 385 (1995)
  97. Georges A et al Rev. Mod. Phys. 68 13 (1996)
  98. Tasaki H J. Phys. Condens. Matter 10 4353 (1998)
  99. Bulut N Adv. Phys. 51 1587 (2002)
  100. Mattheiss L F Phys. Rev. Lett. 58 1028 (1987)
  101. Jorgensen J D et al Phys. Rev. Lett. 58 1024 (1987)
  102. Yu J, Freeman A J, Xu J-H Phys. Rev. Lett. 58 1035 (1987)
  103. Siegrist T et al Phys. Rev. B 35 7137 (1987)
  104. Fulde P Electron Correlations In Molecules And Solids (Springer Series In Solid-State Sciences, Vol. 100) (Berlin: Springer-Verlag, 1991)
  105. Varma C M, Schmitt-Rink S, Abrahams E Solid State Commun. 62 681 (1987)
  106. Nücker N et al Z. Phys. B 67 9 (1987)
  107. Hybertsen M S, Schlüter M, Christensen N E Phys. Rev. B 39 9028 (1989)
  108. Eskes H, Tjeng L H, Sawatzky G A Phys. Rev. B 41 288 (1990)
  109. McMahan A K, Annett J F, Martin R M Phys. Rev. B 42 6268 (1990)
  110. Ogata M, Fukuyama H Rep. Prog. Phys. 71 036501 (2008)
  111. Dopf G, Muramatsu A, Hanke W Phys. Rev. B 41 9264 (1990)
  112. Dopf G, Muramatsu A, Hanke W Phys. Rev. Lett. 68 353 (1992)
  113. Imada M J. Phys. Soc. Jpn. 57 3128 (1988)
  114. Elesin V F i dr Zh. Eksp. Teor. Fiz. 99 237 (1991); Elesin V F et al Sov. Phys. JETP 72 133 (1991)
  115. Lin H Q, Hirsch J E, Scalapino D J Phys. Rev. B 37 7359 (1988)
  116. Hirsch J E et al Phys. Rev. Lett. 60 1668 (1988)
  117. Jones D H, Monaghan S J. Phys. Condens. Matter 1 1843 (1989)
  118. Ogata M, Shiba H J. Phys. Soc. Jpn. 57 3074 (1988)
  119. Schmidt H J, Kuramoto Y Phys. Rev. B 42 2562 (1990)
  120. Hirsch J E et al Phys. Rev. B 39 243 (1989)
  121. Fujimori A Phys. Rev. B 39 793(R) (1989)
  122. Annett J F et al Phys. Rev. B 40 2620(R) (1989)
  123. Grant J B, McMahan A K Phys. Rev. Lett. 66 488 (1991)
  124. Nücker N et al Phys. Rev. B 39 6619 (1989)
  125. Romberg H et al Phys. Rev. B 41 2609(R) (1990)
  126. Pompa M et al Physica C 184 102 (1991)
  127. Chen C T et al Phys. Rev. Lett. 68 2543 (1992)
  128. Dagotto E Rev. Mod. Phys. 66 763 (1994)
  129. Gaididei Yu B, Loktev V M Phys. Status Solidi B 147 307 (1988)
  130. Weber W Z. Phys. B 70 323 (1988)
  131. Kamimura H, Matsuno S, Saito R Solid State Commun. 67 363 (1988)
  132. Müller K A Z. Phys. B 80 193 (1990)
  133. Nickel J H, Morris D E, Ager J W (III) Phys. Rev. Lett. 70 81 (1993)
  134. De Leeuw D M et al Physica C 166 133 (1990)
  135. Di Castro C, Feiner L F, Grilli M Phys. Rev. Lett. 66 3209 (1991)
  136. 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)
  137. Chao K A, Spalek J, Oleś A M J. Phys. C 10 L271 (1977)
  138. Hirsch J E Phys. Lett. A 136 153 (1989)
  139. Yushankhai V Yu, Vujicic G M, Zakula R B Phys. Lett. A 151 254 (1990)
  140. Val’kov V V i dr Pis’ma ZhETF 75 450 (2002); Val’kov V V et al JETP Lett. 75 378 (2002)
  141. Val’kov V V et al Mod. Phys. Lett. B 17 441 (2003)
  142. Val’kov V V, Dzebisashvili D M Zh. Eksp. Teor. Fiz. 127 686 (2005); Val’kov V V, Dzebisashvili D M J. Exp. Theor. Phys. 100 608 (2005)
  143. 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)
  144. Val’kov V V, Golovnya A A Zh. Eksp. Teor. Fiz. 134 1167 (2008); Val’kov V V, Golovnya A A J. Exp. Theor. Phys. 107 996 (2008)
  145. Spalek J, Oleś A M, Chao K A Phys. Status Solidi B 108 329 (1981)
  146. Zhang F C Phys. Rev. Lett. 90 207002 (2003)
  147. Abram M et al Phys. Rev. B 88 094502 (2013)
  148. Spalek J, Zegrodnik M, Kaczmarczyk J Phys. Rev. B 95 024506 (2017)
  149. Jefferson J H, Eskes H, Feiner L F Phys. Rev. B 45 7959 (1992)
  150. Lovtsov S V, Yushankhai V Yu Physica C 179 159 (1991)
  151. Schüttler H-B, Fedro A J Phys. Rev. B 45 7588(R) (1992)
  152. Belinicher V I, Chernyshev A L Phys. Rev. B 47 390 (1993)
  153. Belinicher V I, Chernyshev A L Phys. Rev. B 49 9746 (1994)
  154. Belinicher V I, Chernyshev A L, Shubin V A Phys. Rev. B 53 335 (1996)
  155. Feiner L F, Jefferson J H, Raimondi R Phys. Rev. B 53 8751 (1996)
  156. Raimondi R, Jefferson J H, Feiner L F Phys. Rev. B 53 8774 (1996)
  157. Gavrichkov V A i dr Zh. Eksp. Teor. Fiz. 118 422 (2000); Gavrichkov V A et al J. Exp. Theor. Phys. 91 369 (2000)
  158. Gavrichkov V, Borisov A, Ovchinnikov S G Phys. Rev. B 64 235124 (2001)
  159. Ramšak A, Prelovšek P Phys. Rev. B 40 2239 (1989)
  160. Ramšak A, Prelovšek P Phys. Rev. B 42 10415 (1990)
  161. Vonsovskii S V Zh. Eksp. Teor. Fiz. 16 981 (1946); Vonsovsky S V Sov. Phys. JETP 10 468 (1946)
  162. Izyumov Yu A, Kassan-ogly F A, Skryabin Yu N Polevye Metody v Teorii Ferromagnetizma (M.: Nauka, 1974)
  163. Izyumov Yu A, Skryabin Yu N Bazovye Modeli v Teorii Ferromagnetizma (Ekaterinburg: UrO RAN, 2002)
  164. Klee S, Muramatsu A Nucl. Phys. B 473 539 (1996)
  165. Chakravarty S, Halperin B I, Nelson D R Phys. Rev. Lett. 60 1057 (1988)
  166. Chakravarty S, Halperin B I, Nelson D R Phys. Rev. B 39 2344 (1989)
  167. Hasenfratz P, Leutwyler H Nucl. Phys. B 343 241 (1990)
  168. Hasenfratz P, Niedermayer F Phys. Lett. B 268 231 (1991)
  169. Hasenfratz P, Niedermayer F Z. Phys. B 92 91 (1993)
  170. Ding H-Q, Makivić M S Phys. Rev. Lett. 64 1449 (1990)
  171. Aligia A A, Simon M E, Batista C D Phys. Rev. B 49 13061 (1994)
  172. Kondo J Prog. Theor. Phys. 32 37 (1964)
  173. Val’kov V V, Dzebisashvili D M, Barabanov A F Teor. Mat. Fiz. 191 319 (2017); Val’kov V V, Dzebisashvili D M, Barabanov A F Theor. Math. Phys. 191 752 (2017)
  174. Emery V J, Reiter G Phys. Rev. B 38 11938 (1988)
  175. Zhang F C, Rice T M Phys. Rev. B 41 7243 (1990)
  176. Emery V J, Reiter G Phys. Rev. B 41 7247 (1990)
  177. Eskes H, Sawatzky G A, Feiner L F Physica C 160 424 (1989)
  178. Littlewood P B et al Phys. Rev. B 39 12371 (1989)
  179. Schrieffer J R, Wolff P A Phys. Rev. 149 491 (1966)
  180. Bogolyubov N N Lektsii Po Kvantovoi Statistike (Kiev: Naukova dumka, 1949); Per. na angl. yaz., Bogoliubov N N Lectures On Quantum Statistics (London: Macdonald, 1968)
  181. Tyablikov S V Metody Kvantovoi Teorii Magnetizma (M.: Nauka, 1965); Per. na angl. yaz., Tyablikov S V Methods In The Quantum Theory Of Magnetism (New York: Plenum Press, 1967)
  182. Starykh O A, Bonfim O F A, Reiter G F Phys. Rev. B 52 12534 (1995)
  183. Monthoux P, Balatsky A V, Pines D Phys. Rev. Lett. 67 63448 (1991)
  184. Monthoux P, Pines D Phys. Rev. Lett. 69 961 (1992)
  185. Monthoux P, Pines D Phys. Rev. B 47 6069 (1993)
  186. Izyumov Yu A Usp. Fiz. Nauk 169 225 (1999); Izyumov Yu A Phys. Usp. 42 215 (1999)
  187. Chubukov A V, Pines D, Stojković B P J. Phys. Condens. Matter 8 10017 (1996)
  188. Abanov Ar, Chubukov A V Phys. Rev. Lett. 83 1652 (1999)
  189. Abanov Ar, Chubukov A V Phys. Rev. Lett. 84 5608 (2000)
  190. Abanov Ar, Chubukov A V, Finkel’stein A M Europhys. Lett. 54 488 (2001)
  191. Abanov Ar, Chubukov A V, Schmalian J Adv. Phys. 52 119 (2003)
  192. Abanov Ar, Chubukov A V Phys. Rev. Lett. 93 255702 (2004)
  193. Bang Y New J. Phys. 14 043030 (2012)
  194. Wang Y, Chubukov A V Phys. Rev. B 91 195113 (2015)
  195. Tsvelik A M Phys. Rev. B 95 201112(R) (2017)
  196. Classen L, Robinson N J, Tsvelik A M Phys. Rev. B 99 115110 (2019)
  197. Barabanov A F i dr Zh. Eksp. Teor. Fiz. 110 1480 (1996); Barabanov A F et al J. Exp. Theor. Phys. 83 819 (1996)
  198. Barabanov A F, Kuzian R O, Maksimov L A Phys. Rev. B 55 4015 (1997)
  199. Lau B, Berciu M, Sawatzky G A Phys. Rev. Lett. 106 036401 (2011)
  200. Schrieffer J R J. Low Temp. Phys. 99 397 (1995)
  201. Moraghebi M et al Phys. Rev. B 63 214513 (2001)
  202. Moraghebi M, Yunoki S, Moreo A Phys. Rev. Lett. 88 187001 (2002)
  203. Moraghebi M, Yunoki S, Moreo A Phys. Rev. B 66 214522 (2002)
  204. Eremin I, Manske D Low Temp. Phys. 32 519 (2006)
  205. Silva Neto M B Phys. Rev. B 76 033103 (2007)
  206. Digor D F, Moskalenko V A Teor. Mat. Fiz. 130 320 (2002); Digor D F, Moskalenko V A Theor. Math. Phys. 130 271 (2002)
  207. Borisenko S V et al Phys. Rev. Lett. 84 4453 (2000)
  208. Yoshida T et al Phys. Rev. Lett. 91 027001 (2003)
  209. Zhou X J et al Phys. Rev. Lett. 92 187001 (2004)
  210. Yoshida T et al J. Phys. Condens. Matter 19 125209 (2007)
  211. Wells B O et al Phys. Rev. Lett. 74 964 (1995)
  212. Marshall D S et al Phys. Rev. Lett. 76 4841 (1996)
  213. Ronning F et al Phys. Rev. B 67 035113 (2003)
  214. Shen K M et al Phys. Rev. Lett. 93 267002 (2004)
  215. Shen K M et al Phys. Rev. B 75 075115 (2007)
  216. Tobin J G et al Phys. Rev. B 45 5563 (1992)
  217. Abrikosov A A, Campuzano J C, Gofron K Physica C 214 73 (1993)
  218. Gofron K et al Phys. Rev. Lett. 73 3302 (1994)
  219. Dessau D S et al Phys. Rev. Lett. 71 2781 (1993)
  220. King D M et al Phys. Rev. Lett. 73 3298 (1994)
  221. Aebi P et al Phys. Rev. Lett. 72 2757 (1994)
  222. Loeser A G et al Science 273 325 (1996)
  223. Ding H et al Nature 382 51 (1996)
  224. Ding H et al Phys. Rev. Lett. 78 2628 (1997)
  225. Morinari T J. Phys. Soc. Jpn. 88 104707 (2019)
  226. Berciu M Phys. Rev. Lett. 97 036402 (2006)
  227. Val’kov V V, Golovnya A A, Korovushkin M M Pis’ma ZhETF 94 215 (2011); Val’kov V V, Golovnya A A, Korovushkin M M JETP Lett. 94 197 (2011)
  228. Plakida N M, Oudovenko V S Zh. Eksp. Teor. Fiz. 146 631 (2014); Plakida N M, Oudovenko V S J. Exp. Theor. Phys. 119 554 (2014)
  229. Seibold G, Sigmund E, Hizhnyakov V Phys. Rev. B 48 7537 (1993)
  230. Seibold G, Sigmund E, Hizhnyakov V Phys. Rev. B 57 6937 (1998)
  231. Yamase H Phys. Rev. B 75 014514 (2007)
  232. Seibold G Phys. Rev. B 77 235109 (2008)
  233. Gan J Y et al Phys. Rev. B 78 094504 (2008)
  234. Grusdt F et al Phys. Rev. B 99 224422 (2019)
  235. Kane C L, Lee P A, Read N Phys. Rev. B 39 6880 (1989)
  236. Kane C L et al Phys. Rev. B 41 2653(R) (1990)
  237. Martinez G, Horsch P Phys. Rev. B 44 317 (1991)
  238. Khaliullin G, Horsch P Phys. Rev. B 47 462 (1993)
  239. Ramsak A, Horsch P Phys. Rev. B 57 4308 (1998)
  240. Schmitt-Rink S, Varma C M, Ruckenstein A E Phys. Rev. Lett. 60 2793 (1988)
  241. Richard J L, Yushankhai V Yu Phys. Rev. B 47 1103 (1993)
  242. Feng S, Su Z B, Yu L Phys. Rev. B 49 2368 (1994)
  243. Pepino R T, Ferraz A, Kochetov E Phys. Rev. B 77 035130 (2008)
  244. Klosinski A et al Phys. Rev. B 101 035115 (2020)
  245. Nagaev E L Fizika Magnitnykh Poluprovodnikov (M.: Nauka, 1979); Per. na angl. yaz., Nagaev E L Physics Of Magnetic Semiconductors (Moscow: Mir Publ., 1983)
  246. de Gennes P-G Phys. Rev. 118 141 (1960)
  247. Lyons K B et al Phys. Rev. Lett. 60 732 (1988)
  248. Lyons K B et al Phys. Rev. B 37 2353 (1988)
  249. Sugai S, Shamoto S, Sato M Phys. Rev. B 38 6436 (1988)
  250. Blumberg G et al Phys. Rev. B 53 R11930 (1996)
  251. Blumberg G et al Science 278 1427 (1997)
  252. Bourges P et al Phys. Rev. Lett. 79 4906 (1997)
  253. Inui M, Doniach S, Gabay M Phys. Rev. B 38 6631 (1988)
  254. Annet J F et al Phys. Rev. B 40 2620 (1989)
  255. Kondo J, Yamaji K Prog. Theor. Phys. 47 807 (1972)
  256. Shimahara H, Takada S J. Phys. Soc. Jpn. 60 2394 (1991)
  257. Barabanov A F, Berezovskii V M Zh. Eksp. Teor. Fiz. 106 1156 (1994); Barabanov A F, Berezovsky V M J. Exp. Theor. Phys. 79 627 (1994)
  258. Zwanzig R Phys. Rev. 124 983 (1961)
  259. Mori H Prog. Theor. Phys. 33 423 (1965)
  260. Roth L M Phys. Rev. Lett. 20 1431 (1968)
  261. Plakida N M i dr Zh. Eksp. Teor. Fiz. 124 367 (2003); Plakida N M et al J. Exp. Theor. Phys. 97 331 (2003)
  262. Vladimirov A A, Ile D, Plakida N M Teor. Mat. Fiz. 152 538 (2007); Vladimirov A A, Ihle D, Plakida N M Theor. Math. Phys. 152 1331 (2007)
  263. Barabanov A F et al Pis’ma ZhETF 66 173 (1997); Barabanov A F et al JETP Lett. 66 182 (1997)
  264. Sherman A Phys. Rev. B 73 155105 (2006)
  265. Sherman A Eur. Phys. J. B 92 55 (2019)
  266. Sherman A Phys. Scripta 94 055802 (2019)
  267. Sherman A Eur. Phys. J. B 93 168 (2020)
  268. Val’kov V V et al J. Low Temp. Phys. 197 34 (2019)
  269. Mermin N D, Wagner H Phys. Rev. Lett. 17 1133 (1966)
  270. Barabanov A F, Mikheenkov A V, Shvartsberg A V Teor. Mat. Fiz. 168 389 (2011); Barabanov A F, Mikheenkov A V, Shvartsberg A V Theor. Math. Phys. 168 1192 (2011)
  271. Marshall W Proc. R. Soc. Lond. A 232 48 (1955)
  272. Izyumov Yu A, Medvedev M V Zh. Eksp. Teor. Fiz. 59 553 (1971); Izyumov Y A, Medvedev M V Sov. Phys. JETP 32 302 (1971)
  273. Val’kov V V, Dzebisashvili D M, Barabanov A F J. Supercond. Nov. Magn. 29 1049 (2016)
  274. Keimer B et al Phys. Rev. B 46 14034 (1992)
  275. Barzykin V, Pines D Phys. Rev. B 52 13585 (1995)
  276. Barabanov A F, Maksimov L A, Mikheenkov A V Pis’ma ZhETF 74 362 (2001); Barabanov A F, Maksimov L A, Mikheenkov A V JETP Lett. 74 328 (2001)
  277. Val’kov V, Korovushkin M J. Phys. Soc. Jpn. 80 014703 (2011)
  278. Val’kov V V, Korovushkin M M Zh. Eksp. Teor. Fiz. 139 126 (2011); Val’kov V V, Korovushkin M M J. Exp. Theor. Phys. 112 108 (2011)
  279. Wollman D A et al Phys. Rev. Lett. 71 2134 (1993)
  280. Van Harlingen D J Rev. Mod. Phys. 67 515 (1995)
  281. Scalapino D J Phys. Rep. 250 329 (1995)
  282. Tsuei C C, Kirtley J R Rev. Mod. Phys. 72 969 (2000)
  283. Plakida N M, Oudovenko V S Eur. Phys. J. B 86 115 (2013)
  284. Plakida N M Physica C 531 39 (2016)
  285. Plakida N M Physica C 549 69 (2018)
  286. Zaitsev R O "Issledovanie perekhoda metall - dielektrik" Preprint №IAE-3927/1 (M.: IAE AN SSSR, 1984)
  287. Fröhlich H Phys. Rev. 79 845 (1950)
  288. Tolmachev V V Dokl. Akad. Nauk SSSR 140 563 (1961)
  289. Val’kov V V et al J. Low Temp. Phys. 191 408 (2018)
  290. Fischer M H, Kim E-A Phys. Rev. B 84 144502 (2011)
  291. Val’kov V V et al J. Magn. Magn. Mat. 440 123 (2017)
  292. Zubarev D N Usp. Fiz. Nauk 81 71 (1960); Zubarev D N Sov. Phys. Usp. 3 320 (1960)
  293. Val’kov V V, Dzebisashvili D M, Barabanov A F J. Low Temp. Phys. 181 134 (2015)
  294. Val’kov V V, Korovushkin M M, Barabanov A F J. Low Temp. Phys. 196 242 (2019)
  295. Val’kov V V i dr Zh. Eksp. Teor. Fiz. 155 1045 (2019); Val’kov V V et al J. Exp. Theor. Phys. 128 885 (2019)
  296. Eremin M V, Malakhov M A Pis’ma ZhETF 105 680 (2017); Eremin M V, Malakhov M A JETP Lett. 105 710 (2017)
  297. Eremin M V, Kochergin D S, Malakhov M A Pis’ma ZhETF 108 810 (2018); Eremin M V, Kochergin D S, Malakhov M A JETP Lett. 108 796 (2018)
  298. Carbotte J P et al Phys. Rev. B 81 014522 (2010)
  299. Eremin M V, Syunyaev D A Pis’ma ZhETF 103 209 (2016); Eremin M V, Sunyaev D A JETP Lett. 103 190 (2016)
  300. Hardy W N et al Phys. Rev. Lett. 70 3999 (1993)
  301. Khasanov R et al Phys. Rev. Lett. 98 057007 (2007)
  302. Wojek B M et al Phys. Rev. B 84 144521 (2011)
  303. Sonier J E et al Phys. Rev. Lett. 83 4156 (1999)
  304. Khasanov R et al Phys. Rev. Lett. 99 237601 (2007)
  305. Anukool W et al Phys. Rev. B 80 024516 (2009)
  306. Eremin M V, Larionov I A, Lyubin I E J. Phys. Condens. Matter 22 185704 (2010)
  307. Schrieffer J R Theory Of Superconductivity (New York: W.A. Benjamin, 1964); Per. na russk. yaz., Shriffer D Teoriya Sverkhprovodimosti (M.: Nauka, 1970)
  308. Sadovskii M V Diagrammatika. Lektsii Po Izbrannym Zadacham Teorii Kondensirovannogo Sostoyaniya (Izhevsk: RKhD, 2010)
  309. Tinkham M Introduction To Superconductivity (New York: McGraw-Hill, 1996); Per. na russk. yaz., Tinkkham M Vvedenie v Sverkhprovodimost’ (M.: Atomizdat, 1980)
  310. Bozovic I et al Nature 536 309 (2016)
  311. Panagopoulos C et al Phys. Rev. B 60 14617 (1999)
  312. Lemberger T R et al Phys. Rev. B 82 214513 (2010)
  313. Raghu S et al Phys. Rev. B 85 024516 (2012)
  314. Kagan M Yu i dr Pis’ma ZhETF 97 253 (2013); Kagan M Yu et al JETP Lett. 97 226 (2013)
  315. Kagan M Yu i dr Zh. Eksp. Teor. Fiz. 144 837 (2013); Kagan M Yu et al J. Exp. Theor. Phys. 117 728 (2013)
  316. Val’kov V V i dr FNT 44 173 (2018); Val’kov V V et al Low Temp. Phys. 44 130 (2018)
  317. Barabanov A F, Belemuk A M Pis’ma ZhETF 87 725 (2008); Barabanov A F, Belemuk A M JETP Lett. 87 628 (2004)
  318. Kuchinskii E Z, Sadovskii M V Zh. Eksp. Teor. Fiz. 117 613 (2000); Kuchinskii E Z, Sadovskii M V J. Exp. Theor. Phys. 90 535 (2000)
  319. Kuchinskii E Z, Sadovskii M V Zh. Eksp. Teor. Fiz. 119 553 (2001); Kuchinskii E Z, Sadovskii M V J. Exp. Theor. Phys. 92 480 (2001)
  320. Kuchinskii E Z, Sadovskii M V Zh. Eksp. Teor. Fiz. 121 758 (2002); Kuchinskii E Z, Sadovskii M V J. Exp. Theor. Phys. 94 654 (2002)
  321. Sadovskii M V et al Phys. Rev. B 72 155105 (2005)
  322. Kuchinskii E Z, Nekrasov I A, Sadovskii M V Phys. Rev. B 75 115102 (2007)
  323. Kuchinskii E Z, Nekrasov I A, Sadovskii M V Usp. Fiz. Nauk 182 345 (2012); Kuchinskii E Z, Nekrasov I A, Sadovskii M V Phys. Usp. 55 325 (2012)
  324. Belemuk A M, Barabanov A F, Maksimov L A Pis’ma ZhETF 79 195 (2004); Belemuk A M, Barabanov A F, Maksimov L A JETP Lett. 79 160 (2004)
  325. Belemuk A M, Barabanov A F, Maksimov L A Zh. Eksp. Teor. Fiz. 129 493 (2006); Belemuk A M, Barabanov A F, Maksimov L A J. Exp. Theor. Phys. 102 431 (2006)
  326. Belemuk A M, Barabanov A F, Maksimov L A Pis’ma ZhETF 86 374 (2007); Belemuk A M, Barabanov A F, Maksimov L A JETP Lett. 86 321 (2007)
  327. Belemuk A M, Barabanov A F Pis’ma ZhETF 82 827 (2005); Belemuk A M, Barabanov A F JETP Lett. 82 731 (2005)
  328. Larionov I A, Barabanov A F Pis’ma ZhETF 100 811 (2014); Larionov I A, Barabanov A F JETP Lett. 100 712 (2014)
  329. Barabanov A F i dr Usp. Fiz. Nauk 185 479 (2015); Barabanov A F et al Phys. Usp. 58 446 (2015)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions