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Physical review. B, Condensed matter

Quasi-one-dimensional disordered bipolaronic superconductor

Naoto Nagaosa

Published Feb 1, 1989• 8 citations
Publisher

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.

DOI
10.1103/physrevb.39.2188

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We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles.
We perform an analytical and numerical study of a superconducting instability in quasi-one-dimensional (quasi-1D) disordered systems. Modeling them as an array of Luttinger liquids with Josephson-type interchain coupling, we employed renormalization-group analysis with an extensive search for parameters that support superconductivity enhancement. We have found that this phenomenon is possible in the parameters range that support a latent disorder-driven phase transition between charge- and spin-density-wave phases. Our results may explain the experimental observation of disorder-enhanced superconductivity.