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Low-temperature anomaly in disordered superconductors near Bc2 as a vortex-glass property

An Author Correction to this article was published on 30 October 2018

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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.

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Fig. 1: Low-temperature anomaly of the upper critical field.
Fig. 2: Critical current density near T = 0 and Bc2(0).
Fig. 3: Scaling of the critical current density with magnetic field, jc versus \(\left| {B_{\mathrm{c}}^{j_{\mathrm{c}}} - B} \right|\).
Fig. 4: Vortex de-pinning and thermal creep.
Fig. 5: Disorder dependence of the low-temperature anomaly.

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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

  1. 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)).

    Google Scholar 

  2. Maki, K. Critical fluctuation of the order parameter in a superconductor. I. Prog. Theor. Phys. 40, 193–200 (1968).

    Article  ADS  Google Scholar 

  3. Tenhover, M., Johnson, W. L. & Tsuei, C. C. Upper critical fields of amorphous transition metal based alloys. Solid State Commun. 38, 53–57 (1981).

    Article  ADS  Google Scholar 

  4. Okuma, S., Komori, F., Ootuka, Y. & Kobayashi, S.-I. Superconducting properties of disordered films of Zn. J. Phys. Soc. Jpn. 52, 2639–2641 (1983).

    Article  ADS  Google Scholar 

  5. Hebard, A. F. & Paalanen, M. A. Pair-breaking model for disorder in two-dimensional superconductors. Phys. Rev. B 30, 4063–4066 (1984).

    Article  ADS  Google Scholar 

  6. Graybeal, J. M. & Beasley, M. R. Localization and interaction effects in ultrathin amorphous superconducting films. Phys. Rev. B 29, 4167–4169 (1984).

    Article  ADS  Google Scholar 

  7. 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).

    Article  ADS  Google Scholar 

  8. Nordström, A., Dahlborg, U. & Rapp, Ö. Variation of disorder in superconducting glassy metals. Phys. Rev. B 48, 12866–12873 (1993).

    Article  ADS  Google Scholar 

  9. Sacépé, B. et al. High-field termination of a Cooper-pair insulator. Phys. Rev. B 91, 220508(R) (2015).

    Article  ADS  Google Scholar 

  10. 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).

    Article  ADS  Google Scholar 

  11. 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).

    Article  ADS  Google Scholar 

  12. Xing, Y. et al. Quantum Griffiths singularity of superconductor–metal transition in Ga thin films. Science 350, 542–545 (2015).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Galitski, V. M. & Larkin, A. I. Disorder and quantum fluctuations in superconducting films in strong magnetic fields. Phys. Rev. Lett. 87, 087001 (2001).

    Article  ADS  Google Scholar 

  15. 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).

    Article  ADS  Google Scholar 

  16. Sadovskii, M. V. Superconductivity and localization. Phys. Rep. 282, 225–348 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  17. Smith, R. A., Handy, B. S. & Ambegaokar, V. Upper critical field in disordered two-dimensional superconductors. Phys. Rev. B 61, 6352–6359 (2000).

    Article  ADS  Google Scholar 

  18. 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).

    Article  ADS  Google Scholar 

  19. Galitski, V. M. & Larkin, A. I. Superconducting fluctuations at low temperature. Phys. Rev. B 63, 174506 (2001).

    Article  ADS  Google Scholar 

  20. Galitski, V. Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point. Phys. Rev. Lett. 100, 127001 (2008).

    Article  ADS  Google Scholar 

  21. 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).

    Article  ADS  Google Scholar 

  22. 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).

    Article  ADS  Google Scholar 

  23. 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).

    Article  ADS  Google Scholar 

  24. 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)).

    ADS  Google Scholar 

  25. 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).

    Article  ADS  Google Scholar 

  26. Park, T. et al. Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5. Nature 440, 65–68 (2006).

    Article  ADS  Google Scholar 

  27. 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)).

    MathSciNet  Google Scholar 

  28. 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).

    Article  ADS  Google Scholar 

  29. Larkin, A. I. & Ovchinnikov, Y. N. Collective pinning. Physica B+C 126, 187–192 (1984).

    Article  ADS  Google Scholar 

  30. 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).

    Article  ADS  Google Scholar 

  31. Kwok, W.-K. et al. Vortices in high-performance high-temperature superconductors. Rep. Progr. Phys. 79, 116501 (2016).

    Article  ADS  Google Scholar 

  32. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. 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).

    ADS  Google Scholar 

  37. 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).

  38. Strnad, A. R., Hempstead, C. F. & Kim, Y. B. Dissipative mechanism in type-II superconductors. Phys. Rev. Lett. 13, 794–797 (1964).

    Article  ADS  Google Scholar 

  39. Xiao, Z. L. et al. Edge and bulk transport in the mixed state of a type-II superconductor. Phys. Rev. B 65, 094511 (2002).

    Article  ADS  Google Scholar 

  40. 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).

    Article  ADS  Google Scholar 

  41. Kotliar, G., Sompolinsky, H. & Zippelius, A. Rotational symmetry breaking in Heisenberg spin glasses: A microscopic approach. Phys. Rev. B 35, 311–328 (1987).

    Article  ADS  Google Scholar 

  42. 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).

    MathSciNet  Google Scholar 

  43. Feigel’man, M. V. & Ioffe, L. B. Theory of diamagnetism in granular superconductors. Phys. Rev. Lett. 74, 3447–3450 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. 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).

    Article  Google Scholar 

  46. Campbell, A. M. The response of pinned flux vortices to low-frequency fields. J. Phys. C 2, 1492–1501 (1969).

    Article  ADS  Google Scholar 

  47. Campbell, A. M. The interaction distance between flux lines and pinning centres. J. Phys. C 4, 3186–3198 (1971).

    Article  ADS  Google Scholar 

  48. 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).

    Article  ADS  Google Scholar 

  49. 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).

    Article  ADS  Google Scholar 

  50. Schneider, T. & Schmidt, A. Dimensional crossover scaling in the layered xy-model and 4He films. J. Phys. Soc. Jpn. 61, 2169–2172 (1992).

    Article  ADS  Google Scholar 

  51. Ambegaokar, V., Halperin, B. I., Nelson, D. R. & Siggia, E. D. Dynamics of superfluid films. Phys. Rev. B 21, 1806–1826 (1980).

    Article  ADS  Google Scholar 

  52. Williams, G. A. Dimensionality crossover of the 4He superfluid transition in a slab geometry. J. Low. Temp. Phys. 101, 415–420 (1995).

    Article  ADS  Google Scholar 

  53. Schultka, N. & Manousakis, E. Crossover from two- to three-dimensional behavior in superfluids. Phys. Rev. B 51, 11712–11720 (1995).

    Article  ADS  Google Scholar 

  54. Tinkham, M. Introduction to Superconductivity (Dover, Mineola, 1996).

  55. 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).

    Article  ADS  Google Scholar 

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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.

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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.

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Correspondence to Benjamin Sacépé.

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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

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