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

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.