Effects of strong disorder in strongly correlated superconductors

Abstract

We investigate the effect of strong disorder on a system with strong electronic repulsion. In absence of disorder, the system has a d-wave superconducting ground-state with strong non-BCS features due to its proximity to a Mott insulator. We find that, while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. The suppression of charge motion in regions of strong potential fluctuation leads to formation of Mott insulating patches, which anchor a larger non-superconducting region around them. The system thus breaks into islands of Mott insulating and superconducting regions, with Anderson insulating regions occurring along the boundary of these regions. Thus, electronic correlation and disorder, when both are strong, aid each other in destroying superconductivity, in contrast to their competition at weak disorder. Our results shed light on why Zinc impurities are efficient in destroying superconductivity in cuprates, even though it is robust to weaker impurities.Strong inter-particle interactions and strong inhomogeneous potentials both tend to localize fermions. Strong repulsion can result in complete suppression of charge motion at commensurate filling, leading to a Mott insulator [1], while strong disorder, causes decoherence of fermions triggering formation of Anderson insulators [2]. There is some evidence that weak disorder in presence of strong interactions [3][4][5][6][7] as well as strong disorder in presence of weak interactions [8] compete with each other, but the question of strong disorder in presence of strong repulsion remains unresolved. This is not merely an issue of theoretical interest, since the complex interplay of electronic interactions and disorder in twodimensional (2D) materials is often crucial to understanding novel phenomena [9][10][11][12][13][14] beyond the standard paradigm of Fermi liquid and BCS superconductivity.A prototype of strongly interacting electronic systems is the cuprate high T c superconductors (HTSC), which are antiferromagnetic Mott insulators at half-filling (one particle per site) and show d-wave superconductivity for a range of doping. In this paper, we will consider the effect of strong disorder on the strongly interacting d-wave superconducting (SC) state proximal to the Mott insulator. Our key findings are: (i) While the presence of strong correlations makes superconductivity robust to weak disorder, at large disorder comparable to bandwidth, superconductivity is rapidly suppressed. (ii) At large disorder, Mott insulating patches anchor a surrounding region akin to Anderson insulator. With increasing disorder strength, these islands grow at the expense of local superconductivity. Thus at large disorder, strong correlation and strong potential fluctuations help each other in bringing about the sudden death of superconductivity. The three distinct regions leave clear signatures in the local density of states. Our results shed ...

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Pairing theory for strongly correlated d -wave superconductors

“…We introduce disorder by redefining H t−J to H t−J + iσ (V i − µ)n iσ , where µ is the chemical potential that fixes the average density of electrons, ρ = N −1 iσ n iσ , in the system to a desired value. Such a simple re-definition of the Hamiltonian upon inclusion of disorder, however, would not work for strong disorder (V ≥ 3t) and a modified treatment of Schrieffer-Wolff transformation 47,52 is necessary. Here, we use the model of Box-disorder, where V i 's on all sites i of the lattice are drawn from a uniform 'box' distribution, such that,…”

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