Impurity and interface bound states in $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ superconductors

TL;DR

This paper investigates impurity and interface bound states in certain fully gapped unconventional superconductors, providing analytical results and local density of states calculations relevant for scanning tunnelling microscopy.

Contribution

It analytically derives bound state energies and characterizes local density of states for $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ superconductors, including comparisons with nodal pairing states.

Findings

Bound states form near impurities and interfaces.

Analytical expressions for bound state energies are obtained.

Local density of states features are characterized for experimental detection.

Abstract

Motivated by recent discoveries of novel superconductors such as Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of quasi-particle scattering due to impurities and interfaces for possible gapful $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ Cooper pairing. A bound state appears near a local impurity, and a band of bound states form near an interface. We obtained analytically the bound state energy, and calculated the space and energy dependent local density of states resolvable by high-resolution scanning tunnelling microscopy. For comparison we also sketch results of impurity and surface states if the pairing is nodal p- or d-wave.