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arXiv:1903.11086 · Physical review. B./Physical review. B

Criticality across the energy spectrum from random artificial gravitational lensing in two-dimensional Dirac superconductors

Sayed Ali Akbar Ghorashi, Jonas F. Karcher, Seth M. Davis, Matthew S. Foster

Published Jun 25, 2020• 16 citations
arXivHTMLPDF

Abstract

We numerically study weak, random, spatial velocity modulation [quenched gravitational disorder (QGD)] in two-dimensional massless Dirac materials. QGD couples to the spatial components of the stress tensor; the gauge-invariant disorder strength is encoded in the quenched curvature. Although it is expected to produce negligible effects, wave interference due to QGD transforms all but the lowest-energy states into a quantum-critical ``stack'' with universal, energy-independent spatial fluctuations. We study five variants of velocity disorder, incorporating three different local deformations of the Dirac cone: flattening or steepening of the cone, pseudospin rotations, and nematic deformation (squishing) of the cone. QGD should arise for nodal excitations in the $d$-wave cuprate superconductors (SCs) due to gap inhomogeneity. Our results may explain the division between low-energy ``coherent'' (plane-wave-like) and finite-energy ``incoherent'' (spatially inhomogeneous) excitations in the SC and pseudogap regimes. The model variant that best matches the cuprate phenomenology possesses quenched random pseudospin rotations and nematic fluctuations. This model variant and another with pure nematic randomness exhibit a robust energy swath of stacked critical states, the width of which increases with increasing disorder strength. By contrast, quenched fluctuations that isotropically flatten or steepen the Dirac cone tend to produce strong disorder effects, with more rarefied wave functions at low and high energies. Our models also describe the surface states of class DIII topological SCs.

DOI
10.1103/physrevb.101.214521

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Gapless nodal quasiparticles emerge at a low-energy regime of high-Tc{T}_{c}Tc​ cuprate superconductors due to the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap symmetry. We study the unusual renormalizations of the Fermi velocity vF{v}_{F}vF​ and gap velocity ${v}_{\ensuremath{\Delta}}$ of these quasiparticles close to various quantum critical points in a superconducting dome. Special attention is paid to the behavior of the velocity ratio, ${v}_{\ensuremath{\Delta}}/{v}_{F}$, since it determines a number of observable quantities. We perform a renormalization-group analysis and show that the velocity ratio may vanish, approach unity, or diverge at different quantum critical points. The corresponding superfluid densities and critical temperatures are suppressed, slightly increased, or significantly enhanced. The effects of three types of static disorders, namely, random mass, random gauge potential, and random chemical potential, on the stability of the system are also addressed. An analogous analysis reveals that both random mass and random gauge potential are irrelevant. This implies that these fixed points of the velocity ratio are stable, and hence observable effects ignited by them are unchanged. However, the random chemical potential is marginal. As a result, these fixed points are broken, and thus, the instabilities of quantum phase transitions are triggered.
We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional ddd-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 quasiextended 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.
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