Theoretical studies of the interplay between superconductivity and disorder

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In this thesis, I explore a variety of disordered condensed matter systems and investigate questions pertinent to transport in such systems. In the first part of the thesis, I seek explanations for the strange feature of a giant magnetoresistance peak seen in the vicinity of superconductor-insulator transitions. To this end, I propose a semiclassical two-component Coulomb glass model for 2D insulators close to such transitions. I show that a local pairing attraction in Coulomb glasses can lead to crucial modification of the low-energy density of states which may affect transport. In another explanation for the peak, I consider an Anderson insulator of localized pairs and develop a theory of their transport. I study the change in localization length of the pairs (treated as bosons) on applying a magnetic field and the consequent change in transport properties. I show that from a statistical consideration alone, one can predict a nonmonotonicity in magnetoresistance. In the process, I also revisit the classic problem of directed polymers in a random media (DPRM) and propose a toy model for magnetoresistance in bosonic insulators based on DPRM scalings. In the second part of the thesis, I derive a class of exact solutions for two-level systems driven by a time-periodic external field which pertains to loss mechanisms in superconducting charge qubits.