Abstract
Strongly disordered superconductors in a magnetic field exhibit many characteristic properties of type-II superconductivity—except at low temperatures, where an anomalous linear temperature dependence of the resistive critical field Bc2 is routinely observed. This behaviour violates the conventional theory of superconductivity, and its origin has posed a long-standing puzzle. Here we report systematic measurements of the critical magnetic field and current on amorphous indium oxide films with various levels of disorder. Surprisingly, our measurements show that the Bc2 anomaly is accompanied by mean-field-like scaling of the critical current. Based on a comprehensive theoretical study we argue that these observations are a consequence of the vortex-glass ground state and its thermal fluctuations. Our theory further predicts that the linear-temperature anomaly occurs more generally in both films and disordered bulk superconductors, with a slope that depends on the normal-state sheet resistance, which we confirm experimentally.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Change history
30 October 2018
In the version of this Article originally published, equation (5) was incorrect; see the correction notice for details. This has been corrected in all versions of the Article.
References
Abrikosov, A. A. & Gor’kov, L. P. Contribution to the theory of superconducting alloys with paramagnetic impurities. Zh. Eksp. Teor. Fiz. 39, 1781 (1960). (Sov. Phys. JETP 12, 1243 (1961)).
Maki, K. Critical fluctuation of the order parameter in a superconductor. I. Prog. Theor. Phys. 40, 193–200 (1968).
Tenhover, M., Johnson, W. L. & Tsuei, C. C. Upper critical fields of amorphous transition metal based alloys. Solid State Commun. 38, 53–57 (1981).
Okuma, S., Komori, F., Ootuka, Y. & Kobayashi, S.-I. Superconducting properties of disordered films of Zn. J. Phys. Soc. Jpn. 52, 2639–2641 (1983).
Hebard, A. F. & Paalanen, M. A. Pair-breaking model for disorder in two-dimensional superconductors. Phys. Rev. B 30, 4063–4066 (1984).
Graybeal, J. M. & Beasley, M. R. Localization and interaction effects in ultrathin amorphous superconducting films. Phys. Rev. B 29, 4167–4169 (1984).
Furubayashi, T., Nishida, N., Yamaguchi, M., Morigaki, K. & Ishimoto, H. Superconducting properties of amorphous Si1−xAux near metal–insulator transition. Solid State Commun. 55, 513–516 (1985).
Nordström, A., Dahlborg, U. & Rapp, Ö. Variation of disorder in superconducting glassy metals. Phys. Rev. B 48, 12866–12873 (1993).
Sacépé, B. et al. High-field termination of a Cooper-pair insulator. Phys. Rev. B 91, 220508(R) (2015).
Ren, Z. et al. Anomalous metallic state above the upper critical field of the conventional three-dimensional superconductor AgSnSe2 with strong intrinsic disorder. Phys. Rev. B 87, 064512 (2013).
Bustarret, E. et al. Dependence of the superconducting transition temperature on the doping level in single-crystalline diamond films. Phys. Rev. Lett. 93, 237005 (2004).
Xing, Y. et al. Quantum Griffiths singularity of superconductor–metal transition in Ga thin films. Science 350, 542–545 (2015).
Spivak, B. & Zhou, F. Mesoscopic effects in disordered superconductors near H c2. Phys. Rev. Lett. 74, 2800–2803 (1995).
Galitski, V. M. & Larkin, A. I. Disorder and quantum fluctuations in superconducting films in strong magnetic fields. Phys. Rev. Lett. 87, 087001 (2001).
Coffey, L., Levin, K. & Muttalib, K. A. Upper critical field of strongly disordered three-dimensional superconductors: localization effects. Phys. Rev. B 32, 4382–4391 (1985).
Sadovskii, M. V. Superconductivity and localization. Phys. Rep. 282, 225–348 (1997).
Smith, R. A., Handy, B. S. & Ambegaokar, V. Upper critical field in disordered two-dimensional superconductors. Phys. Rev. B 61, 6352–6359 (2000).
Kim, H. et al. Effect of magnetic Gd impurities on the superconducting state of amorphous Mo–Ge thin films with different thickness and morphology. Phys. Rev. B 86, 024518 (2012).
Galitski, V. M. & Larkin, A. I. Superconducting fluctuations at low temperature. Phys. Rev. B 63, 174506 (2001).
Galitski, V. Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point. Phys. Rev. Lett. 100, 127001 (2008).
Misra, S., Urban, L., Kim, M., Sambandamurthy, G. & Yazdani, A. Measurements of the magnetic-field-tuned conductivity of disordered two-dimensional Mo43Ge57 and InOx superconducting films: evidence for a universal minimum superfluid response. Phys. Rev. Lett. 110, 037002 (2013).
Welp, U., Kwok, W. K., Crabtree, G. W., Vandervoort, K. G. & Liu, J. Z. Magnetic measurements of the upper critical field of Ba2Cu3O7−δ single crystals. Phys. Rev. Lett. 62, 1908–1911 (1989).
Golubov, A. A. & Dorin, V. V. The upper critical field of thin superconducting films with large resistance. J. Low Temp. Phys. 78, 375–386 (1990).
Mikitik, G. P. Temperature dependence of the upper critical field of type II superconductors with fluctuation effects. Zh. Eksp. Teor. Fiz. 101, 1042–1055 (1992). (Sov. Phys. JETP 74, 558–564 (1992)).
Osofsky, M. S. et al. Anomalous temperature dependence of the upper critical magnetic field in Bi–Sr–Cu–O. Phys. Rev. Lett. 71, 2315–2318 (1994).
Park, T. et al. Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5. Nature 440, 65–68 (2006).
Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems. Zh. Eksp. Teor. Fiz. 59, 907–920 (1970). (Sov. Phys. JETP 32, 493–500 (1971)).
Kosterlitz, J. M. & Thouless, D. J. Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory). J. Phys. C 5, L124–L126 (1972).
Larkin, A. I. & Ovchinnikov, Y. N. Collective pinning. Physica B+C 126, 187–192 (1984).
Blatter, G., Feigel’man, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994).
Kwok, W.-K. et al. Vortices in high-performance high-temperature superconductors. Rep. Progr. Phys. 79, 116501 (2016).
Fisher, D. S., Fisher, M. P. A. & Huse, D. A. Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors. Phys. Rev. B 43, 130–159 (1991).
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. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).
Feigel’man, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010).
Mkrtchyan, G. S. & Shmidt, V. V. Interaction between a cavity and a vortex in a superconductor of the second kind. Sov. Phys. JETP 34, 195–197 (1972).
Buchacek, M., Willa, R., Geshkenbein, V. B. & Blatter, G. Thermal depinning and creep in strong pinning theory. Preprint at https://arxiv.org/abs/1802.00652 (2018).
Strnad, A. R., Hempstead, C. F. & Kim, Y. B. Dissipative mechanism in type-II superconductors. Phys. Rev. Lett. 13, 794–797 (1964).
Xiao, Z. L. et al. Edge and bulk transport in the mixed state of a type-II superconductor. Phys. Rev. B 65, 094511 (2002).
Thomann, A. U., Geshkenbein, V. B. & Blatter, G. Dynamical aspects of strong pinning of magnetic vortices in type-II superconductors. Phys. Rev. Lett. 108, 217001 (2012).
Kotliar, G., Sompolinsky, H. & Zippelius, A. Rotational symmetry breaking in Heisenberg spin glasses: A microscopic approach. Phys. Rev. B 35, 311–328 (1987).
Vinokur, V. M., Ioffe, L. B., Larkin, A. I. & Feigel’man, M. V. System of Josephson junctions as a model of a spin glass. Sov. Phys. JETP 66, 198–210 (1987).
Feigel’man, M. V. & Ioffe, L. B. Theory of diamagnetism in granular superconductors. Phys. Rev. Lett. 74, 3447–3450 (1995).
Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).
Guillamón, I. et al. Enhancement of long-range correlations in a 2D vortex lattice by an incommensurate 1D disorder potential. Nat. Phys. 10, 851–856 (2014).
Campbell, A. M. The response of pinned flux vortices to low-frequency fields. J. Phys. C 2, 1492–1501 (1969).
Campbell, A. M. The interaction distance between flux lines and pinning centres. J. Phys. C 4, 3186–3198 (1971).
Coffey, M. W. & Clem, J. R. Unified theory of effects of vortex pinning and flux creep upon the rf surface impedance of type-II superconductors. Phys. Rev. Lett. 67, 386–389 (1991).
Willa, R., Geshkenbein, V. B. & Blatter, G. Probing the pinning landscape in type-II superconductors via Campbell penetration depth. Phys. Rev. B 93, 064515 (2016).
Schneider, T. & Schmidt, A. Dimensional crossover scaling in the layered xy-model and 4He films. J. Phys. Soc. Jpn. 61, 2169–2172 (1992).
Ambegaokar, V., Halperin, B. I., Nelson, D. R. & Siggia, E. D. Dynamics of superfluid films. Phys. Rev. B 21, 1806–1826 (1980).
Williams, G. A. Dimensionality crossover of the 4He superfluid transition in a slab geometry. J. Low. Temp. Phys. 101, 415–420 (1995).
Schultka, N. & Manousakis, E. Crossover from two- to three-dimensional behavior in superfluids. Phys. Rev. B 51, 11712–11720 (1995).
Tinkham, M. Introduction to Superconductivity (Dover, Mineola, 1996).
Feigel’man, M. V. & Ioffe, L. B. Superfluid density of a pseudogapped superconductor near the superconductor–insulator transition. Phys. Rev. B 92, 100509(R) (2015).
Acknowledgements
We are grateful to V. Geshkenbein, L. Ioffe, T. Klein and M. Skvortsov for useful discussions. We thank I. Tamir and D. Shahar for providing sample ITb1. B.S., J.S. and F.G. acknowledge support from the LANEF framework (ANR-10-LABX-51-01) and the H2020 ERC grant QUEST no. 637815. K.D. and A.R. acknowledge support from NSF grant no. DMR 1611421. The research of K.M was supported by the Israel Science Foundation grant no. 1889/16. The research of M.V.F. was partially supported by a Skoltech NGP grant.
Author information
Authors and Affiliations
Contributions
J.S., K.D., A.R. and B.S. fabricated the samples. F.G. provided technical support for low-temperature set-ups and measurements. B.S., J.S. and M.O. performed the measurements. B.S. and J.S. carried out data analysis. K.M. and M.F. developed the theory. B.S., K.M and M.F. wrote the manuscript. All authors discussed the results and commented on the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
14 pages, 9 figures, 1 table, 16 references
Rights and permissions
About this article
Cite this article
Sacépé, B., Seidemann, J., Gay, F. et al. Low-temperature anomaly in disordered superconductors near Bc2 as a vortex-glass property. Nature Phys 15, 48–53 (2019). https://doi.org/10.1038/s41567-018-0294-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-018-0294-6
This article is cited by
-
Quantum breakdown of superconductivity in low-dimensional materials
Nature Physics (2020)
-
The critical current of disordered superconductors near 0 K
Nature Communications (2020)
-
Observation of a superconducting glass state in granular superconducting diamond
Scientific Reports (2019)