Time-reversal symmetry-breaking states near grain boundaries between d-wave superconductors

In this paper we study the order parameter and density of states near a grain boundary between two d(x)2(-y)2 superconductors. We examine broken time-reversal symmetry near the interface. In particular we show that, under suitable circumstances, time-reversal symmetry must be broken even when the order parameter is purely d(x)2(-y)2 everywhere in space.