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.
This is a preview of subscription content
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).
Goldman, A. M. & Markovic, N. Superconductor-insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (1998).
Larkin, A. I. Superconductor-insulator transitions in films and bulk materials. Ann. Phys. 8, 785–794 (1999).
Finkel’stein, A. M. Superconducting transition temperature in amorphous films. J. Exp. Theor. Phys. Lett. 45, 46–49 (1987).
Finkel’stein, A. M. Suppression of superconductivity in homogeneously disordered systems. Physica B 197, 636–648 (1994).
Fisher, M. P. A. Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990).
Larkin, A. & Varlamov, A. Theory of fluctuations in superconductors (Clarendon, 2005).
Fazio, R. & Van der Zant, H. S. J. Quantum phase transitions and vortex dynamics in superconducting networks. Phys. Rep. 355, 235–334 (2001).
Kapitulnik, A., Kivelson, S. & Spivak, B. Z. Anomalous metals: failed superconductors. Rev. Mod. Phys. 91, 011002 (2019).
Tamir, I. et al. Sensitivity of the superconducting state in thin films. Sci. Adv. 5, eaau3826 (2019).
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).
Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).
Altshuler, B. L. & Aronov, A. G. Electron-Electron Interaction in Disordered Conductors (eds Efros, A. L. & Pollak, M.) 1–153 (Elsevier, 1985).
Hebard, A. F. & Paalanen, M. A. Magnetic-field-tuned superconductor-insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990).
Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).
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).
Gantmakher, V. F. & Dolgopolov, V. T. Superconductor-insulator quantum phase transition. Phys. Usp. 53, 1–49 (2010).
Lin, Y.-H., Nelson, J. & Goldman, A. M. Superconductivity of very thin films: the superconductor–insulator transition. Physica C 514, 130–141 (2015).
Biscaras, J. et al. Multiple quantum criticality in a two-dimensional superconductor. Nat. Mater. 12, 542–548 (2013).
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).
Bollinger, A. T. et al. Superconductor–insulator transition in La2−xCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011).
Allain, A., Han, Z. & Bouchiat, V. Electrical control of the superconducting-to-insulating transition in graphene–metal hybrids. Nat. Mater. 11, 590–594 (2012).
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).
Maekawa, S. & Fukuyama, H. Localization effects in two-dimensional superconductors. J. Phys. Soc. Jpn 51, 1380–1385 (1982).
Takagi, H. & Kuroda, Y. Anderson localization and superconducting transition temperature in two-dimensional systems. Solid State Commun. 41, 643–648 (1982).
Sacépé, B. et al. Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition. Phys. Rev. Lett. 101, 157006 (2008).
Sacépé, B. et al. Pseudogap in a thin film of a conventional superconductor. Nat. Commun. 1, 140 (2010).
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).
Sacépé, B. et al. Localization of preformed cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).
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).
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).
Noat, Y. et al. Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy. Phys. Rev. B 88, 014503 (2013).
Ganguly, R. et al. Magnetic field induced emergent inhomogeneity in a superconducting film with weak and homogeneous disorder. Phys. Rev. B 96, 054509 (2017).
Zhao, K. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys. 15, 904–910 (2019).
Larkin, A. I. & Ovchinnikov, Y. N. Density of states in inhomogeneous superconductors. Sov. Phys. J. Exp. Theor. Phys. 34, 1144–1150 (1972).
Ghosal, A., Randeria, M. & Trivedi, N. Role of spatial amplitude fluctuations in highly disordered s-Wave superconductors. Phys. Rev. Lett. 81, 3940–3943 (1998).
Meyer, J. S. & Simons, B. D. Gap fluctuations in inhomogeneous superconductors. Phys. Rev. B 64, 134516 (2001).
Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).
Skvortsov, M. A. & Feigel’man, M. V. Superconductivity in disordered thin films: giant mesoscopic fluctuations. Phys. Rev. Lett. 95, 057002 (2005).
Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor-insulator transition in disordered superconductors. Nature 449, 876–880 (2007).
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).
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).
Lemarié, G. et al. Universal scaling of the order-parameter distribution in strongly disordered superconductors. Phys. Rev. B 87, 184509 (2013).
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).
Ma, M. & Lee, P. A. Localized superconductors. Phys. Rev. B 32, 5658–5667 (1985).
Kapitulnik, A. & Kotliar, G. Anderson localization and the theory of dirty superconductors. Phys. Rev. Lett. 54, 473–476 (1985).
Kotliar, G. & Kapitulnik, A. Anderson localization and the theory of dirty superconductors. II. Phys. Rev. B 33, 3146–3157 (1986).
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).
Feigelman, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010).
Anderson, P. W. Possible consequences of negative U centers in amorphous materials. J. Phys. Coll. 37, 339–342 (1976).
Cuevas, E. & Kravtsov, V. E. Two-eigenfunction correlation in a multifractal metal and insulator. Phys. Rev. B 76, 235119 (2007).
Evers, F. & Mirlin, A. D. Anderson transitions. Rev. Mod. Phys. 80, 1355–1417 (2008).
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).
Burmistrov, I. S., Gornyi, I. V. & Mirlin, A. D. Superconductor-insulator transitions: phase diagram and magnetoresistance. Phys. Rev. B 92, 014506 (2015).
Sacépé, B. et al. Low-temperature anomaly in disordered superconductors near Bc2 as a vortex-glass property. Nat. Phys. 15, 48–53 (2019).
Skvortsov, M. A., Larkin, A. I. & Feigel’man, M. V. Dephasing in disordered metals with superconductive grains. Phys. Rev. Lett. 92, 247002 (2004).
Spivak, B. & Zhou, F. Mesoscopic effects in disordered superconductors near h c2. Phys. Rev. Lett. 74, 2800–2803 (1995).
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).
Kirkpatrick, T. R. & Belitz, D. Metal-superconductor transition at zero temperature: a case of unusual scaling. Phys. Rev. Lett. 79, 3042–3045 (1997).
Frydman, A. The superconductor insulator transition in systems of ultrasmall grains. Physica C 391, 189–195 (2003).
Carbillet, C. et al. Confinement of superconducting fluctuations due to emergent electronic inhomogeneities. Phys. Rev. B 93, 144509 (2016).
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).
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).
Galitski, V. M. & Larkin, A. I. Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields. Phys. Rev. Lett. 87, 087001 (2001).
Lotnyk, D. Suppression of the superconductivity in ultrathin amorphous Mo78Ge22 films observed by STM. Low Temp. Phys 43, 919–923 (2017).
Dubouchet, T. et al. Collective energy gap of preformed Cooper pairs in disordered superconductors. Nat. Phys. 15, 233–236 (2019).
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).
Skvortsov, M. A. & Feigel’man, M. V. Subgap states in disordered superconductors. J. Exp. Theor. Phys. 117, 487–498 (2013).
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).
Martinis, J. M. & Nahum, M. Effect of environmental noise on the accuracy of Coulomb-blockade devices. Phys. Rev. B 48, 18316–18319 (1993).
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).
Varlamov, A. A. & Dorin, V. V. Fluctuation resistance of josephson junctions. Sov. Phys. J. Exp. Theor. Phys. 57, 1089–1096 (1983).
Mandal, S. Destruction of superconductivity through phase fluctuations in ultrathin a-moge films. Preprint at https://arxiv.org/abs/2003.12398 (2020).
Levitov, L. S. & Shytov, A. V. Semiclassical theory of the Coulomb anomaly. J. Exp. Theor. Phys. Lett. 66, 214 (1997).
Deutscher, G. Coherence and single-particle excitations in the high- temperature superconductors. Nature 397, 410–412 (1999).
Deutscher, G. Andreev–Saint-James reflections: a probe of cuprate superconductors. Rev. Mod. Phys. 77, 109–135 (2005).
Matveev, K. A. & Larkin, A. I. Parity effect in ground state energies of ultrasmall superconducting grains. Phys. Rev. Lett. 78, 3749–3752 (1997).
Shahar, D. & Ovadyahu, Z. Superconductivity near the mobility edge. Phys. Rev. B 46, 10917–10922 (1992).
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).
Mott, N. F. & Davis, E. A. Electronic Properties in Non-Crystalline Materials (Clarendon, 1971).
Anderson, P. W. Random-phase approximation in the theory of superconductivity. Phys. Rev. 112, 1900–1916 (1958).
Feigel’man, M. V., Ioffe, L. B. & Mézard, M. Superconductor-insulator transition and energy localization. Phys. Rev. B 82, 184534 (2010).
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).
Kowal, D. & Ovadyahu, Z. Scale dependent superconductor–insulator transition. Physica C 468, 322–325 (2008).
Spathis, P., Aubin, H., Pourret, A. & Behnia, K. Nernst effect in the phase-fluctuating superconductor InOx. Europhys. Lett. 83, 57005 (2008).
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).
Refael, G. & Altman, E. Strong disorder renormalization group primer and the superfluid-insulator transition. Compt. Rend. Phys 14, 725–739 (2013).
Igloi, F. & Monthus, C. Strong disorder RG approach - a short review of recent developments. Eur. Phys. J. B 91, 290 (2014).
Fisher, D. S. Critical behavior of random transverse-field ising spin chains. Phys. Rev. B 51, 6411–6461 (1995).
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).
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).
Han, Z. et al. Collapse of superconductivity in a hybrid tin-graphene Josephson junction array. Nat. Phys. 10, 380–386 (2014).
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).
Kjaergaard, M. et al. Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction. Phys. Rev. Appl. 7, 034029 (2017).
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).
Barends, R. et al. Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits. Appl. Phys. Lett. 99, 113507 (2011).
Kang, J. et al. On-chip intercalated-graphene inductors for next-generation radio frequency electronics. Nat. Electron. 1, 46–51 (2018).
Douçot, B. & Loffe, L. B. Physical implementation of protected qubits. Rep. Prog. Phys. 75, 072001 (2012).
Brooks, P., Kitaev, A. & Preskill, J. Protected gates for superconducting qubits. Phys. Rev. A 87, 052306 (2013).
Groszkowski, P. et al. Coherence properties of the 0-π qubit. New J. Phys. 20, 043053 (2018).
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).
Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. New. J. Phys 7, 219–219 (2005).
Mooij, J. E. & Nazarov, Y. V. Superconducting nanowires as quantum phase-slip junctions. Nat. Phys. 2, 169–172 (2006).
Astafiev, O. V. et al. Coherent quantum phase slip. Nature 484, 355–358 (2012).
Peltonen, J. T. et al. Coherent dynamics and decoherence in a superconducting weak link. Phys. Rev. B 94, 180508 (2016).
Peltonen, J. T. et al. Hybrid rf SQUID qubit based on high kinetic inductance. Sci. Rep. 8, 10033 (2018).
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).
Kuzmin, R. et al. Quantum electrodynamics of a superconductor-insulator phase transition. Nat. Phys. 15, 930–934 (2019).
Maleeva, N. et al. Circuit quantum electrodynamics of granular aluminum resonators. Nat. Commun. 9, 3889 (2018).
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).
Grünhaupt, L. et al. Granular aluminium as a superconducting material for high-impedance quantum circuits. Nat. Mater. 18, 816–819 (2019).
Levy-Bertrand, F. et al. Electrodynamics of granular aluminum from superconductor to insulator: Observation of collective superconducting modes. Phys. Rev. B 99, 094506 (2019).
Wenyuan, Z. et al. Microresonators Fabricated from High-Kinetic-Inductance Aluminum Films. Phys. Rev. Appl. 11, 011003 (2019).
Kamenov, P. et al. Granular aluminum meandered superinductors for quantum circuits. Preprint at https://arxiv.org/1910.00996v1 (2019).
Feigel’man, M. V. & Ioffe, L. B. Superfluid density of a pseudogapped superconductor near the superconductor-insulator transition. Phys. Rev. B 92, 100509 (2015).
Feigel’man, M. V. & Ioffe, L. B. Microwave properties of superconductors close to the superconductor-insulator transition. Phys. Rev. Lett. 120, 037004 (2018).
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).
Sambandamurthy, G., Engel, L. W., Johansson, A. & Shahar, D. Superconductivity-related insulating behavior. Phys. Rev. Lett. 92, 107005 (2004).
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).
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).
Stewart, M. D., Yin, A., Xu, J. M. & Valles, J. M. Superconducting pair correlations in an amorphous insulating nanohoneycomb film. Science 318, 5854 (2007).
Nguyen, H. Q. et al. Observation of giant positive magnetoresistance in a Cooper pair insulator. Phys. Rev. Lett. 103, 157001 (2009).
Doron, A. Instability of insulators near quantum phase transitions. Phys. Rev. Lett. 119, 247001 (2017).
Ovadia, M., Sacépé, B. & Shahar, D. Electron-phonon decoupling in disordered insulators. Phys. Rev. Lett. 102, 176802 (2009).
Ovadia, M. et al. Evidence for a finite-temperature insulator. Sci. Rep. 5, 13503 (2015).
Caviglia, A. D. et al. Electric field control of the LaAlO3/SrTiO3 interface ground state. Nature 456, 624–627 (2008).
Tsen, A. W. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nat. Phys. 12, 208–212 (2016).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
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).
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181 (1973).
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).
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).
The authors declare no competing interests.
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.
About this article
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
Nature Communications (2022)
Quantum phase transition from superconducting to insulating-like state in a pressurized cuprate superconductor
Nature Physics (2022)
NPG Asia Materials (2021)
Size dependent nature of the magnetic-field driven superconductor-to-insulator quantum-phase transitions
Communications Physics (2021)
npj Quantum Information (2021)