Superconductor-Insulator transition and energy localization

M. V. Feigel'man 1, 2, L. B. Ioffe 1, 3, 4, M. Mézard 3

Physical Review B 82 (2010) 184534

We develop an analytical theory for generic disorder-driven quantum phase transitions. We apply this formalism to the superconductor-insulator transition and we briefly discuss the applications to the order-disorder transition in quantum magnets. The effective spin-1/2 models for these transitions are solved in the cavity approximation which becomes exact on a Bethe lattice with large branching number K >> 1 and weak dimensionless coupling g << 1. The characteristic features of the low temperature phase is a large self-formed inhomogeneity of the order-parameter distribution near the critical point K_{c}(g) where the critical temperature T_{c} of the ordering transition vanishes. Near the quantum critical point, the typical value of the order parameter vanishes exponentially, B_{0}\propto e^{-C/(K-K_{c}(g))}. In the disordered regime, realized at K

  • 1. L.D. Landau Institute for Theoretical Physics,
    Landau Institute for Theoretical Physics
  • 2. Moscow Institute of Physics and Technology (MIPT),
    Moscow Institute of Physics and Technology
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. Department of Physics and Astronomy,
    University of California, Riverside