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.
Highlights
Our understanding of dirty superconductors has been evolving for a few decades
Since we anticipate that a drastic change of the critical temperature is related to the SDW/CDW phase transition, we focus on the regions with Kσ(0) < 1 when, according to Fig. 2, we expect to have a rather sharp boundary between two spingapped phases and transition between them driven by disorder strength
We have studied disorder-induced and enhanced superconductivity in a quasi-1D correlated system using RG equations
Summary
Our understanding of dirty superconductors has been evolving for a few decades now. The original description was based on the Anderson theorem [1] which stated that superconductivity is insensitive to perturbations that do not destroy time-reversal invariance, and, do not break Cooper pairs built from exact eigenfunctions which are time-reversal partners of each other. Later it was realized that the assumption of a homogeneous mean-field pairing function breaks down as the system approaches the Anderson metal-insulator transition [2] These mesoscopic fluctuations of the pairing function eventually destroy superconducting order when the number of attractive electrons in the localization volume falls below one [3]. This superconductor-insulator transition in uniformly (not granulated) disordered systems should occur below the Anderson mobility edge only if the Coulomb interaction can be neglected. Recent research on the interplay between superconducting pairing and disorder led to the observation that if the Coulomb repulsion can be neglected, a new critical superconducting phase close to the mobility edge can be identified. Our research was inspired by the observations [10], we are unable to quantitatively describe all the mentioned features within the standard perturbative renormalization-group (RG) analysis but we will show that all those tendencies are present in the perturbative RG flows implying that our model is adequately reflecting the experiments on quasi-1D materials demonstrating superconductivity
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