Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum breakdown of superconductivity in low-dimensional materials

Abstract

In order to understand the emergence of superconductivity it is useful to study the reverse process and identify the various pathways that lead to its destruction. One way is to increase the amount of disorder, as this leads to an increase in Coulomb repulsion that overpowers the attractive interaction responsible for Cooper pair formation. A second pathway—applicable to uniformly disordered materials—is to utilize the competition between superconductivity and Anderson localization, as this leads to electronic granularity in which phase and amplitude fluctuations of the superconducting order parameter play a role. Finally, a third pathway is to construct an array of superconducting islands coupled by some form of proximity effect that leads from a superconducting state to a state with finite resistivity, which appears like a metallic groundstate. This Review Article summarizes recent progress in understanding of these different pathways, including experiments in low dimensional materials and application in superconducting quantum devices.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: The phase diagrams of 2D superconductors.
Fig. 2: Emergent superconducting granularity.
Fig. 3: Pseudogap and collective gap of preformed Cooper pairs.
Fig. 4: Quantum breakdown of superconductivity in a mesoscopic device.
Fig. 5: Examples of applications of high microwave kinetic inductance materials.

References

  1. 1.

    Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).

    ADS  Google Scholar 

  2. 2.

    Goldman, A. M. & Markovic, N. Superconductor-insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (1998).

    Google Scholar 

  3. 3.

    Larkin, A. I. Superconductor-insulator transitions in films and bulk materials. Ann. Phys. 8, 785–794 (1999).

    MATH  Google Scholar 

  4. 4.

    Finkel’stein, A. M. Superconducting transition temperature in amorphous films. J. Exp. Theor. Phys. Lett. 45, 46–49 (1987).

    Google Scholar 

  5. 5.

    Finkel’stein, A. M. Suppression of superconductivity in homogeneously disordered systems. Physica B 197, 636–648 (1994).

    ADS  Google Scholar 

  6. 6.

    Fisher, M. P. A. Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990).

    ADS  Google Scholar 

  7. 7.

    Larkin, A. & Varlamov, A. Theory of fluctuations in superconductors (Clarendon, 2005).

  8. 8.

    Fazio, R. & Van der Zant, H. S. J. Quantum phase transitions and vortex dynamics in superconducting networks. Phys. Rep. 355, 235–334 (2001).

    ADS  Google Scholar 

  9. 9.

    Kapitulnik, A., Kivelson, S. & Spivak, B. Z. Anomalous metals: failed superconductors. Rev. Mod. Phys. 91, 011002 (2019).

    ADS  MathSciNet  Google Scholar 

  10. 10.

    Tamir, I. et al. Sensitivity of the superconducting state in thin films. Sci. Adv. 5, eaau3826 (2019).

    ADS  Google Scholar 

  11. 11.

    Dutta, S. et al. Extreme sensitivity of the vortex state in a-MoGe films to radio-frequency electromagnetic perturbation. Phys. Rev. B 100, 214518 (2019).

    ADS  Google Scholar 

  12. 12.

    Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).

    ADS  Google Scholar 

  13. 13.

    Altshuler, B. L. & Aronov, A. G. Electron-Electron Interaction in Disordered Conductors (eds Efros, A. L. & Pollak, M.) 1–153 (Elsevier, 1985).

  14. 14.

    Hebard, A. F. & Paalanen, M. A. Magnetic-field-tuned superconductor-insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990).

    ADS  Google Scholar 

  15. 15.

    Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).

    ADS  Google Scholar 

  16. 16.

    Steiner, M. A., Breznay, N. P. & Kapitulnik, A. Approach to a superconductor-to-bose-insulator transition in disordered films. Phys. Rev. B 77, 212501 (2008).

    ADS  Google Scholar 

  17. 17.

    Gantmakher, V. F. & Dolgopolov, V. T. Superconductor-insulator quantum phase transition. Phys. Usp. 53, 1–49 (2010).

    ADS  Google Scholar 

  18. 18.

    Lin, Y.-H., Nelson, J. & Goldman, A. M. Superconductivity of very thin films: the superconductor–insulator transition. Physica C 514, 130–141 (2015).

    ADS  Google Scholar 

  19. 19.

    Biscaras, J. et al. Multiple quantum criticality in a two-dimensional superconductor. Nat. Mater. 12, 542–548 (2013).

    ADS  Google Scholar 

  20. 20.

    Sambandamurthy, G. et al. Power law resistivity behavior in 2D superconductors across the magnetic field-tuned superconductor-insulator transition. Europhys. Lett. 75, 611–617 (2006).

    ADS  Google Scholar 

  21. 21.

    Bollinger, A. T. et al. Superconductor–insulator transition in La2−xCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011).

    ADS  Google Scholar 

  22. 22.

    Allain, A., Han, Z. & Bouchiat, V. Electrical control of the superconducting-to-insulating transition in graphene–metal hybrids. Nat. Mater. 11, 590–594 (2012).

    ADS  Google Scholar 

  23. 23.

    Baturina, T. I., Mironov, A. Y., Vinokur, V. M., Baklanov, M. R. & Strunk, C. Localized superconductivity in the quantum-critical region of the disorder-driven superconductor-insulator transition in TiN thin films. Phys. Rev. Lett. 99, 257003 (2007).

    ADS  Google Scholar 

  24. 24.

    Maekawa, S. & Fukuyama, H. Localization effects in two-dimensional superconductors. J. Phys. Soc. Jpn 51, 1380–1385 (1982).

    ADS  Google Scholar 

  25. 25.

    Takagi, H. & Kuroda, Y. Anderson localization and superconducting transition temperature in two-dimensional systems. Solid State Commun. 41, 643–648 (1982).

    ADS  Google Scholar 

  26. 26.

    Sacépé, B. et al. Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition. Phys. Rev. Lett. 101, 157006 (2008).

    ADS  Google Scholar 

  27. 27.

    Sacépé, B. et al. Pseudogap in a thin film of a conventional superconductor. Nat. Commun. 1, 140 (2010).

    Google Scholar 

  28. 28.

    Mondal, M. et al. Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal-insulator transition. Phys. Rev. Lett. 106, 047001 (2011).

    ADS  Google Scholar 

  29. 29.

    Sacépé, B. et al. Localization of preformed cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).

    Google Scholar 

  30. 30.

    Chand, M. et al. Phase diagram of the strongly disordered s-wave superconductor NbN close to the metal-insulator transition. Phys. Rev. B 85, 014508 (2012).

    ADS  Google Scholar 

  31. 31.

    Sherman, D., Kopnov, G., Shahar, D. & Frydman, A. Measurement of a superconducting energy gap in a homogeneously amorphous insulator. Phys. Rev. Lett. 108, 177006 (2012).

    ADS  Google Scholar 

  32. 32.

    Noat, Y. et al. Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy. Phys. Rev. B 88, 014503 (2013).

    ADS  Google Scholar 

  33. 33.

    Ganguly, R. et al. Magnetic field induced emergent inhomogeneity in a superconducting film with weak and homogeneous disorder. Phys. Rev. B 96, 054509 (2017).

    ADS  Google Scholar 

  34. 34.

    Zhao, K. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys. 15, 904–910 (2019).

    Google Scholar 

  35. 35.

    Larkin, A. I. & Ovchinnikov, Y. N. Density of states in inhomogeneous superconductors. Sov. Phys. J. Exp. Theor. Phys. 34, 1144–1150 (1972).

    ADS  Google Scholar 

  36. 36.

    Ghosal, A., Randeria, M. & Trivedi, N. Role of spatial amplitude fluctuations in highly disordered s-Wave superconductors. Phys. Rev. Lett. 81, 3940–3943 (1998).

    ADS  Google Scholar 

  37. 37.

    Meyer, J. S. & Simons, B. D. Gap fluctuations in inhomogeneous superconductors. Phys. Rev. B 64, 134516 (2001).

    ADS  Google Scholar 

  38. 38.

    Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).

    ADS  Google Scholar 

  39. 39.

    Skvortsov, M. A. & Feigel’man, M. V. Superconductivity in disordered thin films: giant mesoscopic fluctuations. Phys. Rev. Lett. 95, 057002 (2005).

    ADS  Google Scholar 

  40. 40.

    Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor-insulator transition in disordered superconductors. Nature 449, 876–880 (2007).

    ADS  Google Scholar 

  41. 41.

    Bouadim, K., Loh, Y. L., Randeria, M. & Trivedi, N. Single- and two-particle energy gaps across the disorder-driven superconductor-insulator transition. Nat. Phys. 7, 884–889 (2011).

    Google Scholar 

  42. 42.

    Feigel’man, M. V. & Skvortsov, M. A. Universal Broadening of the Bardeen-Cooper-Schrieffer Coherence Peak of Disordered Superconducting Films. Phys. Rev. Lett. 109, 147002 (2012).

    ADS  Google Scholar 

  43. 43.

    Lemarié, G. et al. Universal scaling of the order-parameter distribution in strongly disordered superconductors. Phys. Rev. B 87, 184509 (2013).

    ADS  Google Scholar 

  44. 44.

    Stosiek, M., Lang, B. & Evers, F. Self-consistent-field ensembles of disordered Hamiltonians: efficient solver and application to superconducting films. Phys. Rev. B 101, 144503 (2020).

    ADS  Google Scholar 

  45. 45.

    Ma, M. & Lee, P. A. Localized superconductors. Phys. Rev. B 32, 5658–5667 (1985).

    ADS  Google Scholar 

  46. 46.

    Kapitulnik, A. & Kotliar, G. Anderson localization and the theory of dirty superconductors. Phys. Rev. Lett. 54, 473–476 (1985).

    ADS  Google Scholar 

  47. 47.

    Kotliar, G. & Kapitulnik, A. Anderson localization and the theory of dirty superconductors. II. Phys. Rev. B 33, 3146–3157 (1986).

    ADS  Google Scholar 

  48. 48.

    Feigelman, M. V., Ioffe, L. B., Kravtsov, V. E. & Yuzbashyan, E. A. Eigenfunction fractality and pseudogap state near the superconductor-insulator transition. Phys. Rev. Lett. 98, 027001 (2007).

    ADS  Google Scholar 

  49. 49.

    Feigelman, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010).

    ADS  MATH  Google Scholar 

  50. 50.

    Anderson, P. W. Possible consequences of negative U centers in amorphous materials. J. Phys. Coll. 37, 339–342 (1976).

    Google Scholar 

  51. 51.

    Cuevas, E. & Kravtsov, V. E. Two-eigenfunction correlation in a multifractal metal and insulator. Phys. Rev. B 76, 235119 (2007).

    ADS  Google Scholar 

  52. 52.

    Evers, F. & Mirlin, A. D. Anderson transitions. Rev. Mod. Phys. 80, 1355–1417 (2008).

    ADS  Google Scholar 

  53. 53.

    Burmistrov, I. S., Gornyi, I. V. & Mirlin, A. D. Enhancement of the critical temperature of superconductors by Anderson localization. Phys. Rev. Lett. 108, 017002 (2012).

    ADS  Google Scholar 

  54. 54.

    Burmistrov, I. S., Gornyi, I. V. & Mirlin, A. D. Superconductor-insulator transitions: phase diagram and magnetoresistance. Phys. Rev. B 92, 014506 (2015).

    ADS  Google Scholar 

  55. 55.

    Sacépé, B. et al. Low-temperature anomaly in disordered superconductors near Bc2 as a vortex-glass property. Nat. Phys. 15, 48–53 (2019).

    Google Scholar 

  56. 56.

    Skvortsov, M. A., Larkin, A. I. & Feigel’man, M. V. Dephasing in disordered metals with superconductive grains. Phys. Rev. Lett. 92, 247002 (2004).

    ADS  Google Scholar 

  57. 57.

    Spivak, B. & Zhou, F. Mesoscopic effects in disordered superconductors near h c2. Phys. Rev. Lett. 74, 2800–2803 (1995).

    ADS  Google Scholar 

  58. 58.

    Tikhonov, K. S. & Feigel’man, M. V. Strange metal state near quantum superconductor-metal transition in thin films. Ann. Phys. https://doi.org/10.1016/j.aop.2020.168138 (2020).

  59. 59.

    Kirkpatrick, T. R. & Belitz, D. Metal-superconductor transition at zero temperature: a case of unusual scaling. Phys. Rev. Lett. 79, 3042–3045 (1997).

    ADS  Google Scholar 

  60. 60.

    Frydman, A. The superconductor insulator transition in systems of ultrasmall grains. Physica C 391, 189–195 (2003).

    ADS  Google Scholar 

  61. 61.

    Carbillet, C. et al. Confinement of superconducting fluctuations due to emergent electronic inhomogeneities. Phys. Rev. B 93, 144509 (2016).

    ADS  Google Scholar 

  62. 62.

    Carbillet, C. et al. Spectroscopic evidence for strong correlations between local resistance and superconducting gap in ultrathin NbN films. Preprint at https://arxiv.org/abs/1903.01802v2 (2019).

  63. 63.

    Altshuler, B. L., Aronov, A. G. & Lee, P. A. Interaction effects in disordered Fermi Systems in two dimensions. Phys. Rev. Lett. 44, 1288–1291 (1980).

    ADS  Google Scholar 

  64. 64.

    Galitski, V. M. & Larkin, A. I. Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields. Phys. Rev. Lett. 87, 087001 (2001).

    ADS  Google Scholar 

  65. 65.

    Lotnyk, D. Suppression of the superconductivity in ultrathin amorphous Mo78Ge22 films observed by STM. Low Temp. Phys 43, 919–923 (2017).

    ADS  Google Scholar 

  66. 66.

    Dubouchet, T. et al. Collective energy gap of preformed Cooper pairs in disordered superconductors. Nat. Phys. 15, 233–236 (2019).

    Google Scholar 

  67. 67.

    Szabó, P. et al. Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements. Phys. Rev. B 93, 014505 (2016).

    ADS  Google Scholar 

  68. 68.

    Skvortsov, M. A. & Feigel’man, M. V. Subgap states in disordered superconductors. J. Exp. Theor. Phys. 117, 487–498 (2013).

    ADS  Google Scholar 

  69. 69.

    le Sueur, H. & Joyez, P. Room-temperature tunnel current amplifier and experimental setup for high resolution electronic spectroscopy in millikelvin scanning tunneling microscope experiments. Rev. Sci. Instrum. 77, 123701 (2006).

    ADS  Google Scholar 

  70. 70.

    Martinis, J. M. & Nahum, M. Effect of environmental noise on the accuracy of Coulomb-blockade devices. Phys. Rev. B 48, 18316–18319 (1993).

    ADS  Google Scholar 

  71. 71.

    Fischer, Ø., Kugler, M., Maggio-Aprile, I., Berthod, C. & Renner, C. Scanning tunneling spectroscopy of high-temperature superconductors. Rev. Mod. Phys. 79, 353–419 (2007).

    ADS  Google Scholar 

  72. 72.

    Varlamov, A. A. & Dorin, V. V. Fluctuation resistance of josephson junctions. Sov. Phys. J. Exp. Theor. Phys. 57, 1089–1096 (1983).

    Google Scholar 

  73. 73.

    Mandal, S. Destruction of superconductivity through phase fluctuations in ultrathin a-moge films. Preprint at https://arxiv.org/abs/2003.12398 (2020).

  74. 74.

    Levitov, L. S. & Shytov, A. V. Semiclassical theory of the Coulomb anomaly. J. Exp. Theor. Phys. Lett. 66, 214 (1997).

    Google Scholar 

  75. 75.

    Deutscher, G. Coherence and single-particle excitations in the high- temperature superconductors. Nature 397, 410–412 (1999).

    ADS  Google Scholar 

  76. 76.

    Deutscher, G. Andreev–Saint-James reflections: a probe of cuprate superconductors. Rev. Mod. Phys. 77, 109–135 (2005).

    ADS  Google Scholar 

  77. 77.

    Matveev, K. A. & Larkin, A. I. Parity effect in ground state energies of ultrasmall superconducting grains. Phys. Rev. Lett. 78, 3749–3752 (1997).

    ADS  Google Scholar 

  78. 78.

    Shahar, D. & Ovadyahu, Z. Superconductivity near the mobility edge. Phys. Rev. B 46, 10917–10922 (1992).

    ADS  Google Scholar 

  79. 79.

    Gantmakher, V. F., Golubkov, M. V., Lok, J. G. S. & Geim, A. K. Giant negative magnetoresistance of semi-insulating amorphous indium oxide films in strong magnetic fields. J. Exp. Theor. Phys. 82, 951–958 (1996).

    ADS  Google Scholar 

  80. 80.

    Mott, N. F. & Davis, E. A. Electronic Properties in Non-Crystalline Materials (Clarendon, 1971).

  81. 81.

    Anderson, P. W. Random-phase approximation in the theory of superconductivity. Phys. Rev. 112, 1900–1916 (1958).

    ADS  MathSciNet  Google Scholar 

  82. 82.

    Feigel’man, M. V., Ioffe, L. B. & Mézard, M. Superconductor-insulator transition and energy localization. Phys. Rev. B 82, 184534 (2010).

    ADS  Google Scholar 

  83. 83.

    Carpentier, D. & Le Doussal, P. Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves. Nucl. Phys. B 588, 565–629 (1995).

    ADS  MathSciNet  MATH  Google Scholar 

  84. 84.

    Kowal, D. & Ovadyahu, Z. Scale dependent superconductor–insulator transition. Physica C 468, 322–325 (2008).

    ADS  Google Scholar 

  85. 85.

    Spathis, P., Aubin, H., Pourret, A. & Behnia, K. Nernst effect in the phase-fluctuating superconductor InOx. Europhys. Lett. 83, 57005 (2008).

    ADS  Google Scholar 

  86. 86.

    Pourret, A., Spathis, P., Aubin, H. & Behnia, K. Nernst effect as a probe of superconducting fluctuations in disordered thin films. New J. Phys. 11, 055071 (2009).

    ADS  Google Scholar 

  87. 87.

    Refael, G. & Altman, E. Strong disorder renormalization group primer and the superfluid-insulator transition. Compt. Rend. Phys 14, 725–739 (2013).

    ADS  Google Scholar 

  88. 88.

    Igloi, F. & Monthus, C. Strong disorder RG approach - a short review of recent developments. Eur. Phys. J. B 91, 290 (2014).

    ADS  MathSciNet  Google Scholar 

  89. 89.

    Fisher, D. S. Critical behavior of random transverse-field ising spin chains. Phys. Rev. B 51, 6411–6461 (1995).

    ADS  Google Scholar 

  90. 90.

    Abraham, D. W., Lobb, C. J., Tinkham, M. & Klapwijk, T. M. Resistive transition in two-dimensional arrays of superconducting weak links. Phys. Rev. B 26, 5268–5271 (1982).

    ADS  Google Scholar 

  91. 91.

    Eley, S., Gopalakrishnan, S., Goldbart, P. M. & Mason, N. Approaching zero-temperature metallic states in mesoscopic superconductor–normal–superconductor arrays. Nat. Phys. 8, 59–62 (2012).

    Google Scholar 

  92. 92.

    Han, Z. et al. Collapse of superconductivity in a hybrid tin-graphene Josephson junction array. Nat. Phys. 10, 380–386 (2014).

    Google Scholar 

  93. 93.

    Bøttcher, C. G. L. et al. Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array. Nat. Phys. 14, 1138–1144 (2018).

    Google Scholar 

  94. 94.

    Kjaergaard, M. et al. Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction. Phys. Rev. Appl. 7, 034029 (2017).

    ADS  Google Scholar 

  95. 95.

    Martinis, J. M., Devoret, M. H. & Clarke, J. Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction. Phys. Rev. B 35, 4682–4698 (1987).

    ADS  Google Scholar 

  96. 96.

    Barends, R. et al. Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits. Appl. Phys. Lett. 99, 113507 (2011).

    ADS  Google Scholar 

  97. 97.

    Kang, J. et al. On-chip intercalated-graphene inductors for next-generation radio frequency electronics. Nat. Electron. 1, 46–51 (2018).

    Google Scholar 

  98. 98.

    Douçot, B. & Loffe, L. B. Physical implementation of protected qubits. Rep. Prog. Phys. 75, 072001 (2012).

    ADS  MathSciNet  Google Scholar 

  99. 99.

    Brooks, P., Kitaev, A. & Preskill, J. Protected gates for superconducting qubits. Phys. Rev. A 87, 052306 (2013).

    ADS  Google Scholar 

  100. 100.

    Groszkowski, P. et al. Coherence properties of the 0-π qubit. New J. Phys. 20, 043053 (2018).

    ADS  Google Scholar 

  101. 101.

    Smith, W. C., Kou, A., Xiao, X., Vool, U. & Devoret, M. H. Superconducting circuit protected by two-Cooper-pair tunneling. npj Quant. Inf 6, 8 (2020).

    ADS  Google Scholar 

  102. 102.

    Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. New. J. Phys 7, 219–219 (2005).

    ADS  MathSciNet  Google Scholar 

  103. 103.

    Mooij, J. E. & Nazarov, Y. V. Superconducting nanowires as quantum phase-slip junctions. Nat. Phys. 2, 169–172 (2006).

    Google Scholar 

  104. 104.

    Astafiev, O. V. et al. Coherent quantum phase slip. Nature 484, 355–358 (2012).

    ADS  Google Scholar 

  105. 105.

    Peltonen, J. T. et al. Coherent dynamics and decoherence in a superconducting weak link. Phys. Rev. B 94, 180508 (2016).

    ADS  Google Scholar 

  106. 106.

    Peltonen, J. T. et al. Hybrid rf SQUID qubit based on high kinetic inductance. Sci. Rep. 8, 10033 (2018).

    ADS  Google Scholar 

  107. 107.

    de Graaf, S. E., Shaikhaidarov, R., Lindstrom, T., Tzalenchuk, A. Y. & Astafiev, O. V. Charge control of blockade of Cooper pair tunneling in highly disordered TiN nanowires in an inductive environment. Phys. Rev. B 99, 205115 (2019).

    ADS  Google Scholar 

  108. 108.

    Kuzmin, R. et al. Quantum electrodynamics of a superconductor-insulator phase transition. Nat. Phys. 15, 930–934 (2019).

    Google Scholar 

  109. 109.

    Maleeva, N. et al. Circuit quantum electrodynamics of granular aluminum resonators. Nat. Commun. 9, 3889 (2018).

    ADS  Google Scholar 

  110. 110.

    Grünhaupt, L. et al. Loss mechanisms and quasiparticle dynamics in superconducting microwave resonators made of thin-film granular aluminum. Phys. Rev. Lett. 121, 117001 (2018).

    ADS  Google Scholar 

  111. 111.

    Grünhaupt, L. et al. Granular aluminium as a superconducting material for high-impedance quantum circuits. Nat. Mater. 18, 816–819 (2019).

    ADS  Google Scholar 

  112. 112.

    Levy-Bertrand, F. et al. Electrodynamics of granular aluminum from superconductor to insulator: Observation of collective superconducting modes. Phys. Rev. B 99, 094506 (2019).

    ADS  Google Scholar 

  113. 113.

    Wenyuan, Z. et al. Microresonators Fabricated from High-Kinetic-Inductance Aluminum Films. Phys. Rev. Appl. 11, 011003 (2019).

    Google Scholar 

  114. 114.

    Kamenov, P. et al. Granular aluminum meandered superinductors for quantum circuits. Preprint at https://arxiv.org/1910.00996v1 (2019).

  115. 115.

    Feigel’man, M. V. & Ioffe, L. B. Superfluid density of a pseudogapped superconductor near the superconductor-insulator transition. Phys. Rev. B 92, 100509 (2015).

    ADS  Google Scholar 

  116. 116.

    Feigel’man, M. V. & Ioffe, L. B. Microwave properties of superconductors close to the superconductor-insulator transition. Phys. Rev. Lett. 120, 037004 (2018).

    ADS  Google Scholar 

  117. 117.

    Gantmakher, V. F., Golubkov, M. V., Dolgopolov, V. T., Shashkin, A. & Tsydynzhapov, G. E. Observation of the parallel-magnetic-field-induced superconductor-insulator transition in thin amorphous InO films. J. Exp. Theor. Phys. Lett. 71, 473–476 (2000).

    Google Scholar 

  118. 118.

    Sambandamurthy, G., Engel, L. W., Johansson, A. & Shahar, D. Superconductivity-related insulating behavior. Phys. Rev. Lett. 92, 107005 (2004).

    ADS  Google Scholar 

  119. 119.

    Steiner, M. & Kapitulnik, A. Superconductivity in the insulating phase above the field-tuned superconductor-insulator transition in disordered indium oxide films. Physica C 422, 16–26 (2005).

    ADS  Google Scholar 

  120. 120.

    Baturina, T. I., Strunk, C., Baklanov, M. R. & Satta, A. Quantum metallicity on the high-field side of the superconductor-insulator transition. Phys. Rev. Lett. 98, 127003 (2007).

    ADS  Google Scholar 

  121. 121.

    Stewart, M. D., Yin, A., Xu, J. M. & Valles, J. M. Superconducting pair correlations in an amorphous insulating nanohoneycomb film. Science 318, 5854 (2007).

    Google Scholar 

  122. 122.

    Nguyen, H. Q. et al. Observation of giant positive magnetoresistance in a Cooper pair insulator. Phys. Rev. Lett. 103, 157001 (2009).

    ADS  Google Scholar 

  123. 123.

    Doron, A. Instability of insulators near quantum phase transitions. Phys. Rev. Lett. 119, 247001 (2017).

    ADS  Google Scholar 

  124. 124.

    Ovadia, M., Sacépé, B. & Shahar, D. Electron-phonon decoupling in disordered insulators. Phys. Rev. Lett. 102, 176802 (2009).

    ADS  Google Scholar 

  125. 125.

    Ovadia, M. et al. Evidence for a finite-temperature insulator. Sci. Rep. 5, 13503 (2015).

    ADS  Google Scholar 

  126. 126.

    Caviglia, A. D. et al. Electric field control of the LaAlO3/SrTiO3 interface ground state. Nature 456, 624–627 (2008).

    ADS  Google Scholar 

  127. 127.

    Tsen, A. W. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nat. Phys. 12, 208–212 (2016).

    Google Scholar 

  128. 128.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    ADS  Google Scholar 

  129. 129.

    Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov. Phys. JETP Lett. 34, 610 (1972).

    Google Scholar 

  130. 130.

    Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181 (1973).

    ADS  Google Scholar 

  131. 131.

    Strongin, M., Thompson, R. S., Kammerer, O. F. & Crow, J. E. Destruction of superconductivity in disordered near-monolayer films. Phys. Rev. B 1, 1078–1091 (1970).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank the participants of the workshop on The Challenge of 2-Dimensional Superconductivity (8–12 July 2019, Lorentz Center, University of Leiden) for providing us with up-to-date insight into the various viewpoints on the subject. B.S. has received funding from the European Research Council (ERC) under the H2020 programme (grant no. 637815) and from the French National Research Agency (ANR grant CP-Insulator). M.F. is supported by a Skoltech NGP grant and by the RAS program Advanced Problems in Low Temperature Physics. T.M.K. is supported by a grant from the Russian Science Foundation (no. 17-72-30036) and by the Würzburg-Dresden Center of Excellence on Complexity and Topology in Quantum Matter (CT.QMAT).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Benjamin Sacépé.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Hermann Suderow and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sacépé, B., Feigel’man, M. & Klapwijk, T.M. Quantum breakdown of superconductivity in low-dimensional materials. Nat. Phys. 16, 734–746 (2020). https://doi.org/10.1038/s41567-020-0905-x

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing