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Annual Review of Condensed Matter Physics

Volume 15, 2024

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions

Abstract

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors LiZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSeS, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal -wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as -wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

Keyword(s): 2D, BCS, BEC, crossover, phase transitions, quantum phases, topology
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/content/journals/10.1146/annurev-conmatphys-032922-115341
2024-03-11
2025-04-29
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Literature Cited

  1. 1.
    Nakagawa Y, Kasahara Y, Nomoto T, Arita R, Nojima T, Iwasa Y. 2021. Science 372:190–95
     [Google Scholar]
  2. 2.
    Heyl M, Adachi K, Itahashi YM, Nakagawa Y, Kasahara Y et al. 2022. Nat. Commun. 13:6986
     [Google Scholar]
  3. 3.
    Kim H, Choi Y, Lewandowski C, Thomson A, Zhang Y et al. 2022. Nature 606:7914494–500
     [Google Scholar]
  4. 4.
    Park JM, Cao Y, Watanabe K, Taniguchi T, Jarillo-Herrero P. 2021. Nature 590:249–55
     [Google Scholar]
  5. 5.
    Hao Z, Zimmerman AM, Ledwith P, Khalaf E, Najafabai DH et al. 2021. Science 371:65341133–38
     [Google Scholar]
  6. 6.
    Kasahara S, Watashige T, Hanaguri T, Kohsaka Y, Yamashita T et al. 2014. PNAS 111:4616309–13
     [Google Scholar]
  7. 7.
    Hanaguri T, Kasahara S, Böker J, Eremin I, Shibauchi T, Matsuda Y. 2019. Phys. Rev. Lett. 122:077001
     [Google Scholar]
  8. 8.
    Hashimoto T, Ota Y, Tsuzuki A, Nagashima T, Fukushima A et al. 2020. Sci. Adv. 6:eabb9052
     [Google Scholar]
  9. 9.
    Mizukami Y, Haze M, Tanaka O, Matsuura K, Sano D et al. 2023. Commun. Phys. 6:183
     [Google Scholar]
  10. 10.
    Sobirey L, Luick N, Bohlen M, Biss H, Moritz H, Lompe T. 2021. Science 372:6544844–46
     [Google Scholar]
  11. 11.
    Sobirey L, Biss H, Luick N, Bohlen M, Moritz H, Lompe T. 2022. Phys. Rev. Lett. 129:8083601
     [Google Scholar]
  12. 12.
    Bardeen J, Cooper LN, Schrieffer JR. 1957. Phys. Rev. 108:51175–204
     [Google Scholar]
  13. 13.
    Schafroth MR, Butler ST, Blatt JM. 1957. Helv. Phys. Acta 30:93–134
     [Google Scholar]
  14. 14.
    Blatt JM. 1964. Theory of Superconductivity New York: Academic
     [Google Scholar]
  15. 15.
    Leggett AJ. 1980. Modern Trends in the Theory of Condensed Matter, Proc. XVI Karpacz Winter School of Theoretical Physics A Pekalski, JA Przystawa 13–27 Berlin: Springer-Verlag
     [Google Scholar]
  16. 16.
    Leggett AJ. 1980. J. Phys. Colloq. 41:C719–26
     [Google Scholar]
  17. 17.
    Nozières P, Schmitt-Rink S. 1985. J. Low Temp. Phys. 59:3195–211
     [Google Scholar]
  18. 18.
    Sá de Melo CAR, Randeria M, Engelbrecht JR. 1993. Phys. Rev. Lett. 71:193202–5
     [Google Scholar]
  19. 19.
    Engelbrecht JR, Randeria M, Sá de Melo CAR. 1997. Phys. Rev. B 55:2215153–56
     [Google Scholar]
  20. 20.
    Zwierlein MW, Stan CA, Schunck CH, Raupach SMF, Gupta S et al. 2003. Phys. Rev. Lett. 91:25250401
     [Google Scholar]
  21. 21.
    Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S et al. 2003. Science 302:56532101–3
     [Google Scholar]
  22. 22.
    Strecker KE, Partridge GB, Hulet RG. 2003. Phys. Rev. Lett. 91:8080406
     [Google Scholar]
  23. 23.
    Kinast J, Hemmer SL, Gehm ME, Turlapov A, Thomas JE. 2004. Phys. Rev. Lett. 92:150402
     [Google Scholar]
  24. 24.
    Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F et al. 2004. Phys. Rev. Lett. 93:050401
     [Google Scholar]
  25. 25.
    Zwierlein MW, Abo-Shaeer JR, Schirotzek A, Schunck CH, Ketterle W. 2005. Nature 435:70451047–51
     [Google Scholar]
  26. 26.
    Greiner M, Regal CA, Jin DS. 2003. Nature 426:6966537–40
     [Google Scholar]
  27. 27.
    Regal CA, Greiner M, Jin DS. 2004. Phys. Rev. Lett. 92:4040403
     [Google Scholar]
  28. 28.
    Feshbach H. 1958. Ann. Phys. 5:4357–90
     [Google Scholar]
  29. 29.
    Fano U. 1961. Phys. Rev. 124:61866–78
     [Google Scholar]
  30. 30.
    Regal CA, Ticknor C, Bohn JL, Jin DS. 2003. Phys. Rev. Lett. 90:5053201
     [Google Scholar]
  31. 31.
    Gaebler JP, Stewart JT, Bohn JL, Jin DS. 2007. Phys. Rev. Lett. 98:20200403
     [Google Scholar]
  32. 32.
    Botelho SS, Sá de Melo CAR. 2006. Phys. Rev. Lett. 96:040404
     [Google Scholar]
  33. 33.
    Feld M, Fröhlich B, Vogt E, Koschorreck M, Köhl M. 2011. Nature 480:75–78
     [Google Scholar]
  34. 34.
    Bertaina G, Giorgini S. 2011. Phys. Rev. Lett. 106:110403
     [Google Scholar]
  35. 35.
    Fenech K, Dyke P, Peppler T, Lingham M, Hoinka S et al. 2016. Phys. Rev. Lett. 116:045302
     [Google Scholar]
  36. 36.
    Iskin M, Sá de Melo CAR. 2009. Phys. Rev. Lett. 103:165301
     [Google Scholar]
  37. 37.
    Dyke P, Kuhnle ED, Whitlock S, Hu H, Mark M et al. 2011. Phys. Rev. Lett. 106:105304
     [Google Scholar]
  38. 38.
    Sommer AT, Cheuk LW, Ku MJH, Bakr WS, Zwierlein MW. 2011. Phys. Rev. Lett. 108:045302
     [Google Scholar]
  39. 39.
    Ries M, Wenz A, Zürn G, Bayha L, Boettcher I et al. 2011. Phys. Rev. Lett. 114:230401
     [Google Scholar]
  40. 40.
    Boettcher I, Bayha L, Kedar D, Murthy P, Neidig M et al. 2011. Phys. Rev. Lett. 116:045303
     [Google Scholar]
  41. 41.
    Baksmaty LO, Lu H, Bolech CJ, Pu H. 2011. New J. Phys. 13:055014
     [Google Scholar]
  42. 42.
    Imambekov A, Bolech CJ, Lukin M, Demler E. 2006. Phys. Rev. A 74:053626
     [Google Scholar]
  43. 43.
    Mukherjee B, Yan Z, Patel PB, Hadzibabic Z, Yefsah T et al. 2017. Phys. Rev. Lett. 118:12123401
     [Google Scholar]
  44. 44.
    Hueck K, Luick N, Sobirey L, Siegl J, Lompe T, Moritz H. 2018. Phys. Rev. Lett. 120:6060402
     [Google Scholar]
  45. 45.
    Baird L, Wang X, Roof S, Thomas JE. 2019. Phys. Rev. Lett. 123:16160402
     [Google Scholar]
  46. 46.
    Navon N, Smith RP, Hadzibabic Z. 2021. Nat. Phys. 17:1334–41
     [Google Scholar]
  47. 47.
    Schumacher GL, Mäkinen JT, Ji Y, Assumpção GG, Chen J et al. 2023. arxiv:2301.02237
  48. 48.
    Botelho SS, Sá de Melo CAR. 2005. Phys. Rev. B 71:134507
     [Google Scholar]
  49. 49.
    Iskin M, Sá de Melo CAR. 2005. Phys. Rev. B 72:22224513
     [Google Scholar]
  50. 50.
    Petrov DS, Baranov MA, Shlyapnikov GV. 2003. Phys. Rev. A 67:031601(R)
     [Google Scholar]
  51. 51.
    Bohlen M, Sobirey L, Luick N, Biss H, Enss T et al. 2020. Phys. Rev. Lett. 124:24240403
     [Google Scholar]
  52. 52.
    Sá de Melo CAR. 2008. Phys. Today 61:1045–51
     [Google Scholar]
  53. 53.
    Duncan RD, Sá de Melo CAR. 2000. Phys. Rev. B 62:149675
     [Google Scholar]
  54. 54.
    Deleted in proof
  55. 55.
    Borkowski LS, Sá de Melo CAR. 2001. Acta Phys. Pol. 99:6691–98
     [Google Scholar]
  56. 56.
    Botelho SS. 2005. BCS-to-BEC quantum phase transition in high-Tc superconductors and fermionic atomic gases: A functional integral approach PhD Thesis Georgia Institute of Technology Atlanta:
     [Google Scholar]
  57. 57.
    Petrov DS, Shlyapnikov GV. 2001. Phys. Rev. A 64:012706
     [Google Scholar]
  58. 58.
    Berezinskii V. 1971. Sov. Phys. JETP 32:3493–500
     [Google Scholar]
  59. 59.
    Kosterlitz JM, Thouless DJ. 1972. J. Phys. C: Solid State Phys. 5:11L124–26
     [Google Scholar]
  60. 60.
    Nelson DR, Kosterlitz JM. 1977. Phys. Rev. Lett. 39:191201–5
     [Google Scholar]
  61. 61.
    Devreese JPA, Tempere J, Sá de Melo CAR. 2014. Phys. Rev. Lett. 113:16165304
     [Google Scholar]
  62. 62.
    Devreese JPA, Tempere J, Sá de Melo CAR. 2015. Phys. Rev. A 92:4043618
     [Google Scholar]
  63. 63.
    Fisher DS, Hohenberg PC. 1988. Phys. Rev. B 37:104936–43
     [Google Scholar]
  64. 64.
    Perali A, Pieri P, Strinati GC. 2004. Phys. Rev. Lett. 93:10100404
     [Google Scholar]
  65. 65.
    Bulgac A. 2007. Phys. Rev. A 76:040502(R)
     [Google Scholar]
  66. 66.
    Zwierlein MW, Schunck CH, Schirotzek A, Ketterle W. 2006. Nature 442:54–58
     [Google Scholar]
  67. 67.
    Zhou Q, Ho TL. 2011. Phys. Rev. Lett. 106:225301
     [Google Scholar]
  68. 68.
    Köhl M. 2022. Machine Learning Based Detection of Phase Transitions. https://www.pi.uni-bonn.de/koehl/en/research/humphry
  69. 69.
    Combescot R, Kagan MY, Stringari S. 2006. Phys. Rev. A 74:4042717
     [Google Scholar]
  70. 70.
    Kurkjian H, Castin Y, Sinatra A. 2016. Phys. Rev. A 93:013623
     [Google Scholar]
  71. 71.
    Van Loon S, Sá de Melo CAR. 2023. Phys. Rev. Lett. 131:113001
     [Google Scholar]
  72. 72.
    Lifshitz IM. 1960. Sov. Phys. JETP 11:1130–35
     [Google Scholar]
  73. 73.
    Randeria M, Duan J, Shien L. 1990. Phys. Rev. B 41:19327–43
     [Google Scholar]
  74. 74.
    Read N, Green D. 2000. Phys. Rev. B 61:10267
     [Google Scholar]
  75. 75.
    Cao G, He L, Huang XG. 2017. Phys. Rev. A 96:6063618
     [Google Scholar]
  76. 76.
    Harrison N, Chan MK. 2022. Phys. Rev. Lett. 129:017001
     [Google Scholar]
  77. 77.
    Sous J, He Y, Kivelson SA. 2023. npj Quantum Mater 8:25
     [Google Scholar]
  78. 78.
    Kayyalha M, Xiao D, Zhang R, Shin J, Jiang J et al. 2020. Science 367:647364–67
     [Google Scholar]
  79. 79.
    Botelho SS, Sá de Melo CAR. 2004. arxiv:cond-mat/0409357
  80. 80.
    Venu V, Xu P, Mamaev M, Corapi F, Bilitewski T et al. 2023. Nature 613:7943262–67
     [Google Scholar]
  81. 81.
    Zwierlein MW, Schirotzek A, Schunck CH, Ketterle W. 2006. Science 311:5760492–96
     [Google Scholar]
  82. 82.
    Liao Ya, Rittner ASC, Paprotta T, Li W, Partridge GB et al. 2006. Science 311:5760492–96
     [Google Scholar]
  83. 83.
    Sá de Melo CAR. 2014. Multi-Condensates Superconductivity (Erice Lectures) Rome: Superstripes. (Abstr.)
     [Google Scholar]
  84. 84.
    Shi T, Zhang W, Sá de Melo CAR. 2022. EPL 139:36003
     [Google Scholar]
  85. 85.
    Iskin M, Sá de Melo CAR. 2005. Phys. Rev. B 72:024512
     [Google Scholar]
  86. 86.
    Iskin M, Sá de Melo CAR. 2006. Phys. Rev. B 74:144517
     [Google Scholar]
  87. 87.
    Tajima H, Yerin Y, Perali A, Pieri P. 2019. Phys. Rev. B 99:18180503
     [Google Scholar]
  88. 88.
    Yerin Y, Tajima H, Pieri P, Perali A. 2019. Phys. Rev. B 100:104528
     [Google Scholar]
  89. 89.
    Shi YR, Zhang W, Sá de Melo CAR. 2022. EPL 139:36004
     [Google Scholar]
  90. 90.
    Köhl M, Moritz H, Stöferle T, Günther K, Esllinger T. 2005. Phys. Rev. Lett. 94:080403
     [Google Scholar]
  91. 91.
    Chin J, Miller D, Liu Y, Stan C, Setiawan W et al. 2006. Nature 443:961–64
     [Google Scholar]
  92. 92.
    Lewandowski C, Lantagne-Hurtubise E, Thomson A, Nadj-Perge S, Alicea J 2022. Phys. Rev. B 107:L020502
     [Google Scholar]
  93. 93.
    Van Loon S, Sá de Melo CAR. 2023. arxiv:2303.05017
  94. 94.
    Hazra T, Verma N, Randeria M. 2019. Phys. Rev. X 9:031049
     [Google Scholar]
  95. 95.
    Shi T, Zhang W, Sá de Melo CAR. 2022. arxiv:2203.05478
  96. 96.
    Shi T, Zhang W, Sá de Melo CAR. 2023. arxiv:2303.10939
  97. 97.
    Hofmann JS, Chowdhury D, Kivelson SA, Berg E. 2022. NPJ Quantum Mater 7:83
     [Google Scholar]
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Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions
Annual Review of Condensed Matter Physics 15, 109 (2024); https://doi.org/10.1146/annurev-conmatphys-032922-115341
/content/journals/10.1146/annurev-conmatphys-032922-115341
/content/journals/10.1146/annurev-conmatphys-032922-115341
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