One-dimensional Surface Bound States in d-wave Superconductors

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We present an exact quantum theory for the bound states in the vicinity of an edge or a line of impurities in a dₓ₂₋y₂ superconductor. For a (110)-surface we show that a finite dispersion of the one dimensional band of bound states leads to a two peak structure in the density of states (DOS). We study the effect of an applied magnetic field and a subdominant idxy order parameter on the DOS and discuss the implications of our results for tunneling experiments.