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Physical Review Research

Disorder-enhanced superconductivity in a quasi-one-dimensional strongly correlated system

Adam Lowe, V. Kagalovsky, I. V. Yurkevich

Published Jul 16, 2021• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physrevresearch.3.033059

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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.
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 study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL's) as a model for stripes in high-Tc{T}_{c}Tc​ compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi-long-ranged along the stripes and short ranged in the transversal direction.
The interplay of interactions and disorder in low-dimensional superconductors supports the formation of multiple quantum phases as possible instabilities of the superconductor-insulator transition (SIT) at a singular quantum critical point. We explore a one-dimensional model which exhibits such a variety of phases in the strongly quantum fluctuations regime. Specifically, we study the effect of weak disorder on a two-leg Josephson ladder with comparable Josephson and charging energies $({E}_{J}\ensuremath{\sim}{E}_{C})$. An additional key feature of our model is the requirement of perfect Z2{\mathbb{Z}}_{2}Z2​ symmetry, respected by all parameters including the disorder. Using a perturbative renormalization-group (RG) analysis, we derive the phase diagram and identify at least one intermediate phase between a full-fledged superconductor and a disorder-dominated insulator. Most prominently, for repulsive interactions on the rungs we identify two distinct mixed phases: In both of them the longitudinal charge mode is a gapless superconductor, however one phase exhibits a dipolar charge density order on the rungs, while the other is disordered. This latter phase is characterized by coexisting superconducting (phase-locked) and charge-ordered rungs, and encompasses the potential of evolving into a Griffith's phase characteristic of the random-field Ising model in the strong disorder limit.
We use the density-matrix renormalization group method to investigate the superconductor-insulator transition (SIT) in disordered quasi-one-dimensional systems. Focusing on the case of an interacting spinful Hamiltonian at quarter filling, we contrast the differences arising in the SIT when the parent noninteracting model features flat or dispersive bands. Furthermore, we unveil the critical disorder amplitude that triggers insulating behavior by comparing disorder distributions that preserve or not SU(2) symmetry. While scaling analysis suggests the transition be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder is the critical disorder nonvanishing. In this sense, the flat-band structure does strengthen superconductivity in the presence of attractive interactions. For both flat- and dispersive-band models, (i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; (ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.
We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical density matrix renormalization group calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose-glass phase, realizing the Giamarchi-Schulz scenario in such a system.
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.