Vortex and Charge BKT Transition in Disordered Superconducting Thin Films

Disorder degrades superconductivity through its twofold effects of reducing the Cooper pair (CP) binding energy and enhancing phase fluctuations. In many systems, there is strong experimental evidence for CP existence above the critical temperature and the predominance of phase fluctuations in the superconductor to insulator transition. We study two outstanding experimental mysteries: 1. the giant positive magnetoresistance and 2. a putative finite temperature insulator transition. Physically, CPs fill the deep wells of the disorder potential and Josephson tunneling connects these islands. We study the evolution of the islands in a magnetic field and construct an effective Josephson junction model with field dependent parameters. We calculate the magnetoresistance and superfluid stiffness in three parameter regimes. Two of these regimes are governed by vortex BKT criticality with strong phase disorder qualitatively affecting critical behavior. Coming to the finite temperature insulator, we show that this transition can be understood as a charge BKT transition. Strong disorder is shown to result in the Vogel-Fulcher-Tammann critical behaviour which we attribute to the freezing phenomenon of charge dipole excitations.