Quantum Theory of Disordered Superconductors - A Replica Approach
Yat Fan Lau
Motivated by the experimental observations of the anomalous metal states in many superconducting thin films systems, this thesis studies the interplay of disorder and interactions in superconductivity. We first demonstrate that the Fermi glass ground state is unstable in first-order perturbation theory under weak, short-ranged interaction, provided all states are localized. This finding elucidates why methods like the Hartree-Fock approximation are adequate to explain local moment formation in repulsive interactions. We then revisit the problem of dirty superconductors using a replica-symmetric BCS (RS-BCS) theory. We apply RS-BCS theory to disordered superconducting grains within the localization length, assuming the macroscopic system consists of weakly coupled grains. Besides disordered potential, We also consider regions with opposite signs of interaction exist in the grains, with net attractive interaction between electrons. Using RS-BCS mean field theory, we compute the phase diagram, tunneling density of states, and superfluid density across disorder strengths. Our results qualitatively agree with prior numerical studies for purely attractive interactions, and suggest a possible Cooper-pair-glass state when interactions of opposite signs nearly cancel.
•Jan 1, 2025•0 citations