Unusual states of inhomogeneousdx2−y2+idxysuperconductors

Abstract

Superconductors whose order parameter violates time-reversal symmetry and parity have unusual properties that set them apart from conventional superconductors. In particular, if translation symmetry is also broken, the superconducting state generates spontaneously a current and a magnetic field. These phenomena are studied using a $d_{x^2-y^2}{+id}_{\mathrm{xy}}$ superconductor as a prototype. Some of the most striking consequences of the symmetry breaking are examined at boundaries and in the presence of pointlike impurities and quasiparticles.