Full text loading...
Review Article
Open Access
Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions
- C.A.R. Sá de Melo1, and Senne Van Loon1
- Vol. 15:109-129 (Volume publication date March 2024) https://doi.org/10.1146/annurev-conmatphys-032922-115341
-
Copyright © 2024 by the author(s).This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information
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 LixZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1−xSx, 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 s-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 d-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.
Article metrics loading...
Literature Cited
-
1.Nakagawa Y, Kasahara Y, Nomoto T, Arita R, Nojima T, Iwasa Y. 2021. Science 372:190–95
-
2.Heyl M, Adachi K, Itahashi YM, Nakagawa Y, Kasahara Y et al. 2022. Nat. Commun. 13:6986
-
3.Kim H, Choi Y, Lewandowski C, Thomson A, Zhang Y et al. 2022. Nature 606:7914494–500
-
4.Park JM, Cao Y, Watanabe K, Taniguchi T, Jarillo-Herrero P. 2021. Nature 590:249–55
-
5.Hao Z, Zimmerman AM, Ledwith P, Khalaf E, Najafabai DH et al. 2021. Science 371:65341133–38
-
6.Kasahara S, Watashige T, Hanaguri T, Kohsaka Y, Yamashita T et al. 2014. PNAS 111:4616309–13
-
7.Hanaguri T, Kasahara S, Böker J, Eremin I, Shibauchi T, Matsuda Y. 2019. Phys. Rev. Lett. 122:077001
-
8.Hashimoto T, Ota Y, Tsuzuki A, Nagashima T, Fukushima A et al. 2020. Sci. Adv. 6:eabb9052
-
9.Mizukami Y, Haze M, Tanaka O, Matsuura K, Sano D et al. 2023. Commun. Phys. 6:183
-
10.Sobirey L, Luick N, Bohlen M, Biss H, Moritz H, Lompe T. 2021. Science 372:6544844–46
-
11.Sobirey L, Biss H, Luick N, Bohlen M, Moritz H, Lompe T. 2022. Phys. Rev. Lett. 129:8083601
-
12.Bardeen J, Cooper LN, Schrieffer JR. 1957. Phys. Rev. 108:51175–204
-
13.Schafroth MR, Butler ST, Blatt JM. 1957. Helv. Phys. Acta 30:93–134
-
14.Blatt JM. 1964. Theory of Superconductivity New York: Academic
-
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
-
16.Leggett AJ. 1980. J. Phys. Colloq. 41:C719–26
-
17.Nozières P, Schmitt-Rink S. 1985. J. Low Temp. Phys. 59:3195–211
-
18.Sá de Melo CAR, Randeria M, Engelbrecht JR. 1993. Phys. Rev. Lett. 71:193202–5
-
19.Engelbrecht JR, Randeria M, Sá de Melo CAR. 1997. Phys. Rev. B 55:2215153–56
-
20.Zwierlein MW, Stan CA, Schunck CH, Raupach SMF, Gupta S et al. 2003. Phys. Rev. Lett. 91:25250401
-
21.Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S et al. 2003. Science 302:56532101–3
-
22.Strecker KE, Partridge GB, Hulet RG. 2003. Phys. Rev. Lett. 91:8080406
-
23.Kinast J, Hemmer SL, Gehm ME, Turlapov A, Thomas JE. 2004. Phys. Rev. Lett. 92:150402
-
24.Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F et al. 2004. Phys. Rev. Lett. 93:050401
-
25.Zwierlein MW, Abo-Shaeer JR, Schirotzek A, Schunck CH, Ketterle W. 2005. Nature 435:70451047–51
-
26.Greiner M, Regal CA, Jin DS. 2003. Nature 426:6966537–40
-
27.Regal CA, Greiner M, Jin DS. 2004. Phys. Rev. Lett. 92:4040403
-
28.Feshbach H. 1958. Ann. Phys. 5:4357–90
-
29.Fano U. 1961. Phys. Rev. 124:61866–78
-
30.Regal CA, Ticknor C, Bohn JL, Jin DS. 2003. Phys. Rev. Lett. 90:5053201
-
31.Gaebler JP, Stewart JT, Bohn JL, Jin DS. 2007. Phys. Rev. Lett. 98:20200403
-
32.Botelho SS, Sá de Melo CAR. 2006. Phys. Rev. Lett. 96:040404
-
33.Feld M, Fröhlich B, Vogt E, Koschorreck M, Köhl M. 2011. Nature 480:75–78
-
34.Bertaina G, Giorgini S. 2011. Phys. Rev. Lett. 106:110403
-
35.Fenech K, Dyke P, Peppler T, Lingham M, Hoinka S et al. 2016. Phys. Rev. Lett. 116:045302
-
36.Iskin M, Sá de Melo CAR. 2009. Phys. Rev. Lett. 103:165301
-
37.Dyke P, Kuhnle ED, Whitlock S, Hu H, Mark M et al. 2011. Phys. Rev. Lett. 106:105304
-
38.Sommer AT, Cheuk LW, Ku MJH, Bakr WS, Zwierlein MW. 2011. Phys. Rev. Lett. 108:045302
-
39.Ries M, Wenz A, Zürn G, Bayha L, Boettcher I et al. 2011. Phys. Rev. Lett. 114:230401
-
40.Boettcher I, Bayha L, Kedar D, Murthy P, Neidig M et al. 2011. Phys. Rev. Lett. 116:045303
-
41.Baksmaty LO, Lu H, Bolech CJ, Pu H. 2011. New J. Phys. 13:055014
-
42.Imambekov A, Bolech CJ, Lukin M, Demler E. 2006. Phys. Rev. A 74:053626
-
43.Mukherjee B, Yan Z, Patel PB, Hadzibabic Z, Yefsah T et al. 2017. Phys. Rev. Lett. 118:12123401
-
44.Hueck K, Luick N, Sobirey L, Siegl J, Lompe T, Moritz H. 2018. Phys. Rev. Lett. 120:6060402
-
45.Baird L, Wang X, Roof S, Thomas JE. 2019. Phys. Rev. Lett. 123:16160402
-
46.Navon N, Smith RP, Hadzibabic Z. 2021. Nat. Phys. 17:1334–41
-
47.Schumacher GL, Mäkinen JT, Ji Y, Assumpção GG, Chen J et al. 2023. arxiv:2301.02237
-
48.Botelho SS, Sá de Melo CAR. 2005. Phys. Rev. B 71:134507
-
49.Iskin M, Sá de Melo CAR. 2005. Phys. Rev. B 72:22224513
-
50.Petrov DS, Baranov MA, Shlyapnikov GV. 2003. Phys. Rev. A 67:031601(R)
-
51.Bohlen M, Sobirey L, Luick N, Biss H, Enss T et al. 2020. Phys. Rev. Lett. 124:24240403
-
52.Sá de Melo CAR. 2008. Phys. Today 61:1045–51
-
53.Duncan RD, Sá de Melo CAR. 2000. Phys. Rev. B 62:149675
-
54.Deleted in proof
-
55.Borkowski LS, Sá de Melo CAR. 2001. Acta Phys. Pol. 99:6691–98
-
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:
-
57.Petrov DS, Shlyapnikov GV. 2001. Phys. Rev. A 64:012706
-
58.Berezinskii V. 1971. Sov. Phys. JETP 32:3493–500
-
59.Kosterlitz JM, Thouless DJ. 1972. J. Phys. C: Solid State Phys. 5:11L124–26
-
60.Nelson DR, Kosterlitz JM. 1977. Phys. Rev. Lett. 39:191201–5
-
61.Devreese JPA, Tempere J, Sá de Melo CAR. 2014. Phys. Rev. Lett. 113:16165304
-
62.Devreese JPA, Tempere J, Sá de Melo CAR. 2015. Phys. Rev. A 92:4043618
-
63.Fisher DS, Hohenberg PC. 1988. Phys. Rev. B 37:104936–43
-
64.Perali A, Pieri P, Strinati GC. 2004. Phys. Rev. Lett. 93:10100404
-
65.Bulgac A. 2007. Phys. Rev. A 76:040502(R)
-
66.Zwierlein MW, Schunck CH, Schirotzek A, Ketterle W. 2006. Nature 442:54–58
-
67.Zhou Q, Ho TL. 2011. Phys. Rev. Lett. 106:225301
-
68.Köhl M. 2022. Machine Learning Based Detection of Phase Transitions. https://www.pi.uni-bonn.de/koehl/en/research/humphry
-
69.Combescot R, Kagan MY, Stringari S. 2006. Phys. Rev. A 74:4042717
-
70.Kurkjian H, Castin Y, Sinatra A. 2016. Phys. Rev. A 93:013623
-
71.Van Loon S, Sá de Melo CAR. 2023. Phys. Rev. Lett. 131:113001
-
72.Lifshitz IM. 1960. Sov. Phys. JETP 11:1130–35
-
73.Randeria M, Duan J, Shien L. 1990. Phys. Rev. B 41:19327–43
-
74.Read N, Green D. 2000. Phys. Rev. B 61:10267
-
75.Cao G, He L, Huang XG. 2017. Phys. Rev. A 96:6063618
-
76.Harrison N, Chan MK. 2022. Phys. Rev. Lett. 129:017001
-
77.Sous J, He Y, Kivelson SA. 2023. npj Quantum Mater 8:25
-
78.Kayyalha M, Xiao D, Zhang R, Shin J, Jiang J et al. 2020. Science 367:647364–67
-
79.Botelho SS, Sá de Melo CAR. 2004. arxiv:cond-mat/0409357
-
80.Venu V, Xu P, Mamaev M, Corapi F, Bilitewski T et al. 2023. Nature 613:7943262–67
-
81.Zwierlein MW, Schirotzek A, Schunck CH, Ketterle W. 2006. Science 311:5760492–96
-
82.Liao Ya, Rittner ASC, Paprotta T, Li W, Partridge GB et al. 2006. Science 311:5760492–96
-
83.Sá de Melo CAR. 2014. Multi-Condensates Superconductivity (Erice Lectures) Rome: Superstripes. (Abstr.)
-
84.Shi T, Zhang W, Sá de Melo CAR. 2022. EPL 139:36003
-
85.Iskin M, Sá de Melo CAR. 2005. Phys. Rev. B 72:024512
-
86.Iskin M, Sá de Melo CAR. 2006. Phys. Rev. B 74:144517
-
87.Tajima H, Yerin Y, Perali A, Pieri P. 2019. Phys. Rev. B 99:18180503
-
88.Yerin Y, Tajima H, Pieri P, Perali A. 2019. Phys. Rev. B 100:104528
-
89.Shi YR, Zhang W, Sá de Melo CAR. 2022. EPL 139:36004
-
90.Köhl M, Moritz H, Stöferle T, Günther K, Esllinger T. 2005. Phys. Rev. Lett. 94:080403
-
91.Chin J, Miller D, Liu Y, Stan C, Setiawan W et al. 2006. Nature 443:961–64
-
92.Lewandowski C, Lantagne-Hurtubise E, Thomson A, Nadj-Perge S, Alicea J 2022. Phys. Rev. B 107:L020502
-
93.Van Loon S, Sá de Melo CAR. 2023. arxiv:2303.05017
-
94.Hazra T, Verma N, Randeria M. 2019. Phys. Rev. X 9:031049
-
95.Shi T, Zhang W, Sá de Melo CAR. 2022. arxiv:2203.05478
-
96.Shi T, Zhang W, Sá de Melo CAR. 2023. arxiv:2303.10939
-
97.Hofmann JS, Chowdhury D, Kivelson SA, Berg E. 2022. NPJ Quantum Mater 7:83
Data & Media loading...
- Article Type: Review Article
Most Read This Month
Most Cited Most Cited RSS feed
-
-
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Vol. 6 (2015), pp. 15–38
-
-
-
-
-
-
-
-
-
-
-
Correlated Quantum Phenomena in the Strong Spin-Orbit Regime
Vol. 5 (2014), pp. 57–82
-
-
-
Interface Physics in Complex Oxide Heterostructures
Vol. 2 (2011), pp. 141–165
-
-
-
-
-
Strong Correlations from Hund’s Coupling
Vol. 4 (2013), pp. 137–178
-
- More Less