Superinsulator and quantum synchronization

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Synchronized oscillators are ubiquitous in nature1, and synchronization plays a key part in various classical and quantum phenomena. Several experiments2,3,4 have shown that in thin superconducting films, disorder enforces the droplet-like electronic texture—superconducting islands immersed into a normal matrix—and that tuning disorder drives the system from superconducting to insulating behaviour. In the vicinity of the transition, a distinct state4 forms: a Cooper-pair insulator, with thermally activated conductivity. It results from synchronization of the phase of the superconducting order parameter at the islands across the whole system5. Here we show that at a certain finite temperature, a Cooper-pair insulator undergoes a transition to a superinsulating state with infinite resistance. We present experimental evidence of this transition in titanium nitride films and show that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage that is analogous to the critical current in superconductors.

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Figure 1: Two-dimensional Josephson junction array.
Figure 2: Conductivity in normal-insulating and superinsulating states.
Figure 3: Magnetic-field-tuned transition to superinsulating state.
Figure 4: Sketch of dual-phase diagrams for a superconductor and a superinsulator.


  1. 1

    Pikovsky, A., Rosenblum, M. & Kurths, J. Synchronization: A Universal Concept in Nonlinear Science (Cambridge Univ. Press, Cambridge, 2001)

  2. 2

    Kowal, D. & Ovadyahu, Z. Disorder induced granularity in an amorphous superconductor. Solid State Commun. 90, 783–786 (1994)

  3. 3

    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 field. Zh. Eksp. Teor. Fiz. 109, 1765–1778 (1996); JETP 82, 951–958 (1996)

  4. 4

    Baturina, T. I., Mironov, A., Yu, 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)

  5. 5

    Fistul, M. V., Vinokur, V. M. & Baturina, T. I. Collective Cooper-pair transport in the insulating state of Josephson junction arrays. Phys. Rev. Lett. 100, 086805 (2008)

  6. 6

    Tinkham, M. Introduction to Superconductivity 2nd edn, Ch. 6 (McGraw-Hill, New York, 1996)

  7. 7

    Beloborodov, I. S., Fominov, V., Lopatin, A. V. & Vinokur, V. M. Insulating state of granular superconductors in a strong-coupling regime. Phys. Rev. B 74, 014502 (2006)

  8. 8

    Lopatin, A. V. & Vinokur, V. M. Hopping transport in granular superconductors. Phys. Rev. B 75, 092201 (2007)

  9. 9

    Mooij, J. E. et al. Unbinding of charge-anticharge pairs in two-dimensional arrays of small tunnel junctions. Phys. Rev. Lett. 65, 645–649 (1990)

  10. 10

    Fazio, R. & Schön, G. Charge and vortex dynamics in arrays of tunnel junctions. Phys. Rev. Lett. 43, 5307–5320 (1991)

  11. 11

    Averin, D. V. & Likharev, K. K. in Mesoscopic Phenomena in Solids (eds Altshuler, B. L. et al.) 173–271 (Elsevier, Amsterdam, 1991)

  12. 12

    Altland, A., Glazman, L. I., Kamenev, A. & Meyer, J. S. Inelastic electron transport in granular arrays. Ann. Phys. 321, 2566–2603 (2006)

  13. 13

    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)

  14. 14

    Ingold, G.-L. & Nazarov in Single Charge Tunneling (eds Grabert, H. & Devoret, M. H.) Vol. 294 21–107 (NATO ASI Series B, Plenum, New York, 1991)

  15. 15

    Landau, L. D. & Lifshitz, E. M. Quantum Mechanics (Non-Relativistic Theory) Ch. 6 142–146 (Elsevier Science, Oxford, UK/ Burlington, Massachusetts, 2003)

  16. 16

    Ingold. G.-L in Quantum Transport and Dissipation (eds Dittrich, T. et al.) Ch. 4 213–248 (Wiley-VCH, Weinheim, 1998)

  17. 17

    Koval, Y., Fistul, M. V. & Ustinov, A. V. Enhancement of Josephson phase diffusion by microwaves. Phys. Rev. Lett. 93, 087004 (2004)

  18. 18

    Matveev, K. A., Gisselfält, M., Glazman, L. I., Jonson, M. & Shekhter, R. I. Parity-induced suppression of the Coulomb blockade of Josephson tunneling. Phys. Rev. Lett. 70, 2940–2943 (1993)

  19. 19

    Lotkhov, S. V., Bogoslovsky, S. A., Zorin, A. B. & Niemeyer, J. Cooper pair cotunneling in single charge transistors with dissipative electromagnetic environment. Phys. Rev. Lett. 91, 197002 (2003)

  20. 20

    Efetov, K. B. & Tschersich, A. Coulomb effects in granular materials at not very low temperatures. Phys. Rev. B 67, 174205 (2003)

  21. 21

    José, J. V., Kadanoff, L. P., Kirkpatrick, S. & Nelson, D. R. Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B 16, 1217–1241 (1997)

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We thank Y. Galperin, V. F. Gantmakher and A. Kamenev for discussions. This work was supported by the US Department of Energy Office of Science, Alexander von Humboldt Foundation, the Russian Foundation for Basic Research, the “Quantum Macrophysics” Program of the Russian Academy of Sciences, and the Deutsche Forschungsgemeinschaft.

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Correspondence to Valerii M. Vinokur.

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