Abstract
In this paper we study the order parameter and density of states near a grain boundary between two ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ 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 ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ everywhere in space.
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