Topological Phase Transitions and New Developments

Abstract

Destruction of superconductivity in thin films was thought to be a simple instance of Berezinskii-Kosterlitz-Thouless physics in which only two phases exist: a superconductor with algebraic long range order in which the vortices condense and an insulator where the vortex-antivortex pairs proliferate. However, since 1989 this view has been challenged as now a preponderance of experiments indicate that an intervening bosonic metallic state obtains upon the destruction of superconductivity. We review here a glassy model which is capable of capturing both of these features. The finite resistance arises from three features. First, the disordered insulator-superconductor transition in the absence of fermionic degrees of freedom (Cooper pairs only), is controlled by a diffusive fixed point\cite{CN} rather than the critical point of the clean system. Hence, the relevant physics that generates the Bose metal should arise from a term in the action in which different replicas are mixed. We show explicitly how such physics arises in the phase glass. Second, in 2D (not in 3D) the phase stiffness of the glass phase vanishes explicitly as has been shown in extensive numerical simulations\cite{ky,kosterlitz1,kosterlitz2}. Third, bosons moving in such a glassy environment fail to localize as a result of the false minima in the landscape. We calculate the conductivity explicitly using Kubo response and show that it turns on as a power law and has a vanishing Hall response as a result of underlying particle-hole symmetry. We show that when particle-hole symmetry is broken, the Hall conductance turns on with the same power law as does the longitudinal conductance.