Superconductor-Insulator transition and energy localization

TL;DR

This paper develops an analytical theory for disorder-driven quantum phase transitions, focusing on the superconductor-insulator transition, revealing inhomogeneity and localization phenomena near criticality.

Contribution

It introduces a formalism for analyzing quantum phase transitions using cavity approximation, uncovering inhomogeneity and localization effects in superconductor-insulator transitions.

Findings

Near the critical point, the order parameter vanishes exponentially.

Two distinct phases are identified in the disordered regime with different localization properties.

The theory explains activated resistivity behavior and tunneling data near the transition.

Abstract

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<K_{c}(g) we find actually two distinct phases characterized by different behavior of relaxation rates. The first phase exists in an intermediate range of K^{*}(g)<K<K_{c}(g). It has two regimes of energies: at low excitation energies, \omega<\omega_{d}(K,g), the many-body spectrum of the model is discrete, with zero level widths, while at \omega>\omega_{d} the level acquire a non-zero width which is self-generated by the many-body interactions. In this phase the spin model provides by itself an intrinsic thermal bath. Another phase is obtained at smaller K<K^{*}(g), where all the eigenstates are discrete, corresponding to full many-body localization. These results provide an explanation for the activated behavior of the resistivity in amorphous materials on the insulating side near the SI transition and a semi-quantitative description of the scanning tunneling data on its superconductive side.