Quasiparticle spectrum of grain boundaries in d-wave superconductors

A grain boundary which separates domains with different orientation along the c-axis is analyzed. The coupling of two parallel superconducting planes whose order parameters are rotated leads to interesting properties which are expected to be common to other kinds of grain boundary. The density of states is enhanced at low energies. The number of localized states depends on the degree of misfit across the boundary. A continuum of zero energy states appears at certain values of the angle rotation.