Fate of disorder-induced inhomogeneities in strongly correlated d-wave superconductors

Abstract

We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local-order parameters change drastically from those obtained in a simple Hartree-Fock-Bogoliubov theory. Although both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find they compete with each other, leading to a relatively smooth variation of the local density. Our self-consistent calculations modify the spatial fluctuations in the pairing amplitude by suppressing all the double occupancy within a Gutzwiller formalism and prohibit the formation of distinct superconducting 'islands'. In contrast, presence of such 'islands' controls the outcome if strong correlations are neglected. The reorganization of the spatial structures in the Gutzwiller method makes these superconductors surprisingly insensitive to the impurities. This is illustrated by a very weak decay of superfluid stiffness, off-diagonal long-range order and local density of states up to a large disorder strength. Exploring the origin of such a robustness, we conclude that the underlying one-particle normal states reshape in a rich manner, such that the superconductor formed by pairing these states experiences a weaker but spatially correlated effective disorder. Such a route to superconductivity is evocative of Andersonʼs theorem. Our results capture the key experimental trends in the cuprates.The study of disordered high-temperature superconductors (HTSC) [1, 2] is scientifically rewarding for multiple reasons. First, we learn to deal with strongly correlated electrons. The significance of strong repulsive correlations is paramount in these superconductors, which make their parent (undoped) compound an antiferromagnetic Mott insulator [3]. Second, the superconductivity in HTSC cuprates is believed to originate from the two-dimensional copperoxide (CuO 2 ) planes [4] and is rife with the complex effects of enhanced quantum fluctuations from the reduced dimensionality [5,6]. Finally, these systems provide an ideal environment for the complex interplay of electronic interactions and disorder [7], both of which are strong. By tuning various parameters describing these systems, including disorder, the cuprates can be made to undergo quantum phase transitions [8] to various non-superconducting phases. Each such quantum phase transition can vastly add to our knowledge of the condensed phases of matter.Although the physics of HTSC is far from being settled for the unusual normal state, the superconductivity in clean systems is well described by a Bardeen-Cooper-Schrieffer (BCS)like ground state (GS) [9] at low temperatures (T). Such BCS-GS is identified with d-wave pairing amplitude [10][11][12] and hence is referred to as a d-wave superconductor (dSC). The corresponding Bogoliubov quasiparticles result in a linear low-lying density of states (DOS) [13]. The effect of impuritie...

Effects of strong disorder in strongly correlated superconductors

“…A semianalytic approach, where effects of projection are kept in terms of renormalization of Hamiltonian parameters, is the Gutzwiller approximation [24], which is known [25] to match the more sophisticated Monte Carlo results [22] for the homogeneous system. This approach is easily extended to inhomogeneous situations to get a renormalized inhomogeneous mean field theory (RIMT) [15,[26][27][28], which tries to capture effects of both strong correlations and disorder in the system.A surprising result of RIMT [15,[26][27][28] is that in-spite of the d-wave nature of the order parameter, strong correlations make superconductivity robust up to moderate disorders. This is ascribed to the electronic repulsions that modify the hopping amplitudes based on local density and smear out charge accumulation near deep potential wells, leading to a much weaker effective disorder.…”

“…In this paper, we will present results on 30 × 30 lattice (with a repeated zone scheme [27, 31] used on 12 × 12 unit cells for better resolution and statistics, see SM). We will express all energies in units of t.Demise of superconducting correlations.--To look at the robustness of SC, we study the off diagonal long range order, [15,27] to make superconductivity rather immune to disorder, as plotted in Fig. 1(a) (dashed line).…”

“…Demise of superconducting correlations.--To look at the robustness of SC, we study the off diagonal long range order, [15,27] to make superconductivity rather immune to disorder, as plotted in Fig. 1(a) (dashed line).…”

“…A surprising result of RIMT [15,[26][27][28] is that in-spite of the d-wave nature of the order parameter, strong correlations make superconductivity robust up to moderate disorders. This is ascribed to the electronic repulsions that modify the hopping amplitudes based on local density and smear out charge accumulation near deep potential wells, leading to a much weaker effective disorder.…”

“…Here x i is the local hole doping which is determined selfconsistently together with a Fock shift (τ ij ) and a d-wave pairing amplitude (∆ ij ) on each bond (See supplementary material (SM) for details). In this paper, we will present results on 30 × 30 lattice (with a repeated zone scheme [27,31] used on 12 × 12 unit cells for better resolution and statistics, see SM). We will express all energies in units of t.…”