Impurity clusters and localization of nodal quasiparticles in \emph{d}-wave superconductors

TL;DR

This paper investigates how magnetic impurities in d-wave superconductors can create a finite density of states at zero energy, leading to localization of quasiparticles and a mobility gap, challenging previous self-consistent predictions.

Contribution

It introduces a group expansion technique showing magnetic impurities cause a finite zero-energy density of states with a power-law dependence on impurity concentration, differing from prior models.

Findings

Finite $ ho(0)$ possible with magnetic impurities.

Zero-energy states are localized on impurity clusters.

Existence of a mobility gap with exponential suppression of low-temperature kinetics.

Abstract

The long disputed issue of the limiting value of quasiparticle density of states $\r(0) = \r (\e \to 0)$ in a \emph{d-}wave superconductor with impurities (\emph{vs} its linear vanishing, $\r_0(\e) \propto |\e|/\D$, near the nodal point $\e = 0$ in a pure system with the gap parameter $\D$) is discussed. Using the technique of group expansions of Green functions in complexes of interacting impurities, it is shown that finite $\r(0)$ value is possible if the (finite) impurity perturbation $V$ is spin-dependent (magnetic). The found value has a power law dependence on the impurity concentration $c$: $\r(0) \propto \r_N c^{n}$, where $\r_N$ is the normal metal density of states and $n \geq 2$ is the least number of impurities in a complex that can localize nodal quasiparticle. This result essentially differs from the known predictions of self-consistent approximation: $\r(0) \propto \r_N \sqrt {c/\r_N\D}$ (for the unitary limit $V \to \infty$) or $\r(0) \propto (\D/cV^2)\exp(-\D/cV^2\r_N)$ (for the Born limit $|V|\r_N \ll 1$). We predict also existence of a narrow interval (mobility gap) around the Fermi energy, where all the states are localized on proper impurity clusters, leading to exponential suppression of low-temperature kinetics.