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

TL;DR

This paper investigates how different types of disorder affect the quasiparticle density of states and localization in cuprate superconductors, revealing that disorder type and concentration significantly influence low-energy electronic properties.

Contribution

It provides a detailed real-space analysis of disorder effects on the DOS and localization in cuprates, incorporating realistic impurity models and their implications.

Findings

Random on-site energy and pointlike impurities suppress DOS at low disorder levels.

Smooth disorder from impurities away from CuO planes creates finite DOS at realistic impurity levels.

States near the Fermi energy are strongly localized with a non-monotonic localization length dependence.

Abstract

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.