Abstract
The investigation is in terms of a generalized scattering matrix approach. A new condition for the existence of interface states is derived under the assumption that each of the two crystals in contact has both a mirror plane and a centre of symmetry on this mirror plane, the interface being chosen parallel to the two mirror planes. The common energy gap obtained from narrow gaps at the centre or edges of the Brillouin zones can obtain, at most, one interface state. By answering the question of the existence of an interface state enables one to simultaneously answer the question of the localization of this interface state in the common energy gap.
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