It is shown that a sizable areal density of midgap states exists on a {110} surface of a ${\mathit{d}}_{\mathit{x}\mathit{a}}^2$-${\mathit{x}}_{\mathit{b}}^2$-wave superconductor, which can either have vacuum or an insulator at the surface, or be separated from vacuum or an insulator by a clean, size-quantized, normal metal overlayer. These ‘‘midgap’’ states have many observable consequences—some of which are briefly discussed here—which can be used as a clear signature to distinguish between d-wave and anisotropic s-wave superconductors.

• Received 27 July 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.1526