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Register a new userFrom immunity to sudden death: Effects of strong disorder in strongly correlated superconductors
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Added by
Debmalya Chakraborty
Publication date
2016
fields
Physics
and research's language is
English
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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.
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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 what are obtained in a simple Hartree-Fock-Bogoliubov theory. While both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find them to 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 Andersons theorem. Our results capture the key experimental trends in the cuprates.
Motivated by recent proposals of correlation induced insensitivity of d-wave superconductors to impurities, we develop a simple pairing theory for these systems for up to a moderate strength of disorder. Our description implements the key ideas of Anderson, originally proposed for disordered s-wave superconductors, but in addition takes care of the inherent strong electronic repulsion in these compounds, as well as disorder induced inhomogeneities. We first obtain the self-consistent one-particle states, that capture the effects of disorder exactly, and strong correlations using Gutzwiller approximation. These `normal states, representing the interplay of strong correlations and disorder, when coupled through pairing attractions following the path of Bardeen-Cooper-Schrieffer (BCS), produce results nearly identical to those from a more sophisticated Gutzwiller augmented Bogoliubov-de Gennes analysis.
The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. Here we show that this interplay in cuprates generates a new phase of matter: a fully gapped phase crystal state that breaks both translational and time reversal invariance, characterized by a modulation of the $d$-wave superconducting phase co-existing with a modulating extended $s$-wave superconducting order. In contrast to conventional wisdom, we find that this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization.
We investigate the effect of thermal fluctuations on the two-particle spectral function for a disordered $s$-wave superconductor in two dimensions, focusing on the evolution of the collective amplitude and phase modes. We find three main effects of thermal fluctuations: (a) the phase mode is softened with increasing temperature reflecting the decrease of superfluid stiffness; (b) remarkably, the non-dispersive collective amplitude modes at finite energy near ${bf q}=[0,0]$ and ${bf q}=[pi,pi]$ survive even in presence of thermal fluctuations in the disordered superconductor; and (c) the scattering of the thermally excited fermionic quasiparticles leads to low energy incoherent spectral weight that forms a strongly momentum-dependent background halo around the phase and amplitude collective modes and broadens them. Due to momentum and energy conservation constraints, this halo has a boundary which disperses linearly at low momenta and shows a strong dip near the $[pi,pi]$ point in the Brillouin zone.
A quantum pseudo-spin model with random spin sizes is introduced to study the effects of charging-energy disorder on the superconducting transition in granular superconducting materials. Charging-energy effects result from the small electrical capacitance of the grains when the Coulomb charging energy is comparable to the Josephson coupling energy. In the pseudo-spin model, randomness in the spin size is argued to arise from the inhomogeneous grain-size distribution. For a particular bimodal spin-size distribution, the model describes percolating granular superconductors. A mean-field theory is developed to obtain the phase diagram as a function of temperature, average charging energy and disorder.
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