Resonant states and order-parameter suppression near point-like impurities in d-wave superconductors

TL;DR

This paper investigates how local suppression of the superconducting order parameter near impurities influences low-energy resonances in d-wave superconductors, revealing that suppression can induce resonances even for weaker impurities.

Contribution

It introduces a model where order-parameter suppression near impurities explains the emergence of resonances at weaker impurity strengths, extending understanding of impurity effects in d-wave superconductors.

Findings

Suppression of the order parameter enhances low-energy resonances.

Resonance position and width depend on the ratio of bandwidth to superconducting gap.

Order-parameter suppression effectively increases impurity strength towards the unitary limit.

Abstract

We examine the role of order-parameter suppression in the development of low-energy peaks (i.e., resonances) in the tunneling density of states near a non-magnetic impurity in a d-wave superconductor. Without order-parameter suppression, the zero-energy resonance appears only in the unitary (i.e., strong impurity) limit. However, suppression makes the resonance appear even when the impurity is much weaker. To model this situation, we make the physical hypothesis that the order parameter is reduced whenever one electron of a Cooper pair encounters the impurity, a hypothesis that retains the exact solvability of the problem. In this way, we determine that suppression of the order parameter drives the effective strength of the impurity towards the unitary limit. We determine the order-parameter reduction variationally, and show that the ratios between the main energy scales--the band width and superconducting gap--strongly affect this reduction and, in consequence, the position and width of the resonance.