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...
The mysterious pseudo-gap (PG) phase of cuprate superconductors has been the subject of intense investigation over the last thirty years, but without a clear agreement about its origin. Owing to a recent observation in Raman spectroscopy, of a precursor in the charge channel, on top of the well known fact of a precursor in the superconducting channel, we present here a novel idea: the PG is formed through a Higgs mechanism, where two kinds of preformed pairs, in the particle-particle and particle-hole channels, become entangled through a freezing of their global phase. Remarkably, this entanglement is equivalent to fractionalizing a bond Cooper pair density wave (PDW) into its elementary parts; the particle-hole pair, giving rise to both density modulations and current modulations, and the particle-particle counterpart, leading to the formation of Cooper pairs. From this perspective, the "fractionalized PDW" becomes the central object around the formation of the pseudo-gap. The "locking" of phases between the charge and superconducting modes gives a unique explanation for the unusual global phase coherence of short-range charge modulations, observed below Tc on phase sensitive scanning tunneling microscopy (STM). A simple microscopic model enables us to estimate the mean-field values of the precursor gaps in each channel and the PG energy scale, and to compare them to the values observed in Raman scattering spectroscopy. We also discuss the possibility of a multiplicity of orders in the PG phase and give an overview of the phase diagram. arXiv:1906.01633v2 [cond-mat.supr-con]
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