Two kinds of heterostructures have been proposed and investigated in this paper. One is called the SCSC heterostructure which is composed of two semi- infinite two dimensional phononic crystals (PCs) consisting of circular cylinders embedded in the square lattice with different filling fractions, and the other is named the RRTC heterostructure, which is composed of two semi- infinite PCs consisting of rectangular cylinders in a rectangular lattice and circular cylinders in a triangular lattice, respectively. The interface guided modes in the PC heterostructures with CCl4 (mercury) cylinders in a mercury (CCl4) host were analysed using the plane-wave expansion method in combination with a supercell technique. The results show that interface states are absent in the simple SCSC heterostructure, but they can be created either by lateral lattice slipping or by increasing the interface separation, and also the absolute gap width and the number of guided modes depends strongly on the relatively transverse displacement and longitudinal gliding. It is anticipated that the guided modes in such heterostructures can be engineered by adjusting the relative transverse or longitudinal displacement. For the RRTC hererostructure, it could generate interface guided modes states without any relative displacement.
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