Quasiparticle Density of States, Localization, and Distributed Disorder in the Cuprate Superconductors

We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional d-wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasi-extended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.Comment: 29 pages, 19 figures, published version, includes minor change

Revisiting Quasiparticle Scattering Interference in High-Temperature Superconductors: The Problem of Narrow Peaks

We revisit the interpretation of quasiparticle scattering interference in cuprate high-$T_c$ superconductors. This phenomenon has been very successful in reconstructing the dispersions of d-wave Bogoliubov excitations, but the successful identification and interpretation of QPI in scanning tunneling spectroscopy (STS) experiments rely on theoretical results obtained for the case of isolated impurities. We introduce a highly flexible technique to simulate STS measurements by computing the local density of states using real-space Green's functions defined on two-dimensional lattices with as many as 100,000 sites. We focus on the following question: to what extent can the experimental results be reproduced when various forms of distributed disorder are present? We consider randomly distributed point-like impurities, smooth "Coulombic" disorder, and disorder arising from random on-site energies and superconducting gaps. We find an apparent paradox: the QPI peaks in the Fourier-transformed local density of states appear to be sharper and better defined in experiment than those seen in our simulations. We arrive at a no-go result for smooth-potential disorder since this does not reproduce the QPI peaks associated with large-momentum scattering. An ensemble of point-like impurities gets closest to experiment, but this goes hand in hand with impurity cores that are not seen in experiment. We also study the effects of possible measurement artifacts (the "fork mechanism"), which turn out to be of relatively minor consequence. It appears that there is an unknown mechanism at work which renders the QPI peaks much sharper than they are based on present theoretical understanding.Comment: 23 pages, 25 figures, published version, includes minor change

Multi-Atom Quasiparticle Scattering Interference for Superconductor Energy-Gap Symmetry Determination

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $\Delta_\mathbf{k}^\alpha$, for all momenta $\mathbf{k}$ on the Fermi surface of every band $\alpha$. While there are a variety of techniques for determining $|\Delta_\mathbf{k}^\alpha|$, no general method existed to measure the signed values of $\Delta_\mathbf{k}^\alpha$. Recently, however, a new technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where $\Delta_\mathbf{k}^\alpha$ has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $\Delta_\mathbf{k}^\alpha$ it generates to the $\Delta_\mathbf{k}^\alpha$ determined from single-atom scattering in FeSe where $s_{\pm}$ energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $\Delta_\mathbf{k}^\alpha$ of opposite sign

Phase-sensitive determination of nodal d-wave order parameter in single-band and multiband superconductors

Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently, a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal d-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized correction to the tunneling density of states due to nonmagnetic impurities in the Born limit and at intermediate-scattering strength shows characteristic features for sign-changing and sign-preserving scattering wave vectors, as well as for the momentum-integrated quantity. Furthermore, using a realistic approach accounting for the Wannier orbitals, we model scanning tunneling microscopy data of Bi2Sr2CaCu2O8+delta, which should allow the comparison of our theory with experimental data

Puddle formation, persistent gaps, and non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+{\delta}

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but it was often thought that the superconductivity at sufficiently high doping is governed by conventional mean-field Bardeen-Cooper-Schrieffer (BCS) theory[1]. However, recent measurements show that the number of paired electrons (the superfluid density) vanishes when the transition temperature Tc goes to zero[2], in contradiction to expectation from BCS theory. The origin of this anomalous vanishing is unknown. Our scanning tunneling spectroscopy measurements in the overdoped regime of the (Pb,Bi)2Sr2CuO6+{\delta} high-temperature superconductor show that it is due to the emergence of puddled superconductivity, featuring nanoscale superconducting islands in a metallic matrix[3,4]. Our measurements further reveal that this puddling is driven by gap filling, while the gap itself persists beyond the breakdown of superconductivity. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair-breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory