Comment on criteria for existence of surface states

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Abstract
Pendrey and Gurman have recently given criteria for the existence of surface at surfaces of reflection summetry. They found for a gap occurring at the face of a Brillouin zone that either zero or one surface state would exist depending upon the sign of a matrix element. We show that they have misinterpreted their criterion in the case that the Brillouin-zone face and crystal face are not parallel and that for the (110) gap in (100) bcc crystals a surface state always exists according to their criterion and in agreement with our calculated results on Li. We then show that the assumption that higher-energy states may be neglected if the energy difference between the gap and those states is much greater than the gap width is not valid. We extend the theory to include the higher-energy states and find that a Brillouin-zone gap may contain more than one surface state. This is in agreement with our detailed energy-band calculations for thin films of Al and Li.