Quasi-one-dimensional disordered bipolaronic superconductor

Abstract

We investigate superconductivity in a quasi-one-dimensional bipolaron system with random potentials, treating the interchain Josephson couplings in the mean-field approximation. The model is transformed into the S=(1/2 XXZ-spin chain with random fields along the z axis and the ordering field along the x axis. Using the quantum transfer-matrix method by the Suzuki-Trotter formula, we calculate the order parameter and the rigidity as functions of the temperature, the mean strength of the random fields, and the ordering field. We obtain the two-parameter scaling laws for these quantities. We also discuss these scaling relations by using the cumulant expansion in the phase Hamiltonian. This analytical method is extended to the more general models of one-dimensional interacting electrons, and the generalized susceptibilities for various long-range orderings are discussed in the light of the scaling laws.

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