**Valerii Vinokur**

Argonne National Laboratory

*Gauge Theory of the Superconductor-Insulator Transition*

The standard model of particle physics is extraordinarily successful at explaining much of the physical realm. Yet, one of its most profound aspects, the mechanism of confinement, that binds quarks into hadrons and which is believed to be mediated by the chromo-electric strings in a condensate of magnetic monopoles [1-3], is not thoroughly understood and lacks direct experimental evidence. We demonstrate that the infinite-resistance superinsulating state [4-7], a mirror analogue of superconductivity, emerging at the insulating side of the superconductor- insulator transition (SIT) [8-12] is a condensed matter realization of the quark confinement. We reveal that the mechanism ensuring the infinite resistance of superinsulators is the binding of Cooper pairs into neutral “mesons” by electric strings and establish a mapping of quarks onto Cooper pairs in superinsulators. We derive the linear confinement of Cooper pairs in both two- and three dimensions, generalizing thus the concept of superinsulation onto 3D systems, and calculate the deconfinement temperature, which in 2D coincides with the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. We reveal a Cooper pair analogue of the asymptotic freedom effect [13] implying that systems smaller than the string scale appear in a quantum metallic state. We construct the phase diagram of the critical vicinity of the SIT and find the criterion for realizing either the direct SIT or the transition via an intermediate Bose metal phase. We unravel, finally, that this Bose metal phase is a topological insulator. Our findings offer a powerful laboratory for exploring fundamental implications of confinement, asymptotic freedom, and related quantum chromodynamics (QCD) phenomena via desktop experiments on superconductors.

References

[1] S. Mandelstam, Phys. Rep. 23, 245–249 (1976).

[2] G. ’t Hooft, in High Energy Physics. Zichichi, A. ed., Editrice Compositori, Bologna (1976).

[3] A. M. Polyakov, Phys. Lett. 59, 82–84 (1975).

[4] M. C. Diamantini, P. Sodano, C. A. Trugenberger, Nucl. Phys. B474, 641–677 (1996).

[5] A. Krämer, S. Doniach, Phys. Rev. Lett. 81, 3523–3527 (1998).

[6] V. M. Vinokur et al, Nature 452, 613–615 (2008).

[7] T. I. Baturina, V. M. Vinokur, Ann. Phys. 331, 236 – 257 (2013).

[8] K. B. Efetov, Sov. Phys. JETP 51, 1015–1022 (1980).

[9] D. Haviland, Y. Liu, A. Goldman, Phys. Rev. Lett. 62, 2180–2183 (1989).

[10] A. Hebard. M. A. Paalanen, Phys. Rev. Lett. 65, 927–930 (1990).

[11] M. P. A. Fisher, G. Grinstein, S. M. Girvin, Phys. Rev. Lett. 64, 587–590 (1990).

[12] R.Fazio, G. Schön, Phys. Rev. B 43, 5307–5320 (1991).

[13] D. Gross, Nucl. Phys. B: Proceedings Supplements 74, 426–446 (1998).