In the present communication, by means of the frequency-dependent plane wave expansion method, we theoretically demonstrate the photonic band structures of a new type of two-dimensional (2D) annular photonic crystals (PCs) called 2D ternary superconductor PCs created by square and triangular lattices. Our idea is based on the appearance of the interfacial layer through a number of experimental works. We mainly investigate the maximization of the photonic band gap (PBG) using two types of ternary superconductor PCs. Type I in which an interfacial layer of Nb low temperature superconductor (LTSC) is encircled by cylindrical rods and a background material of two different dielectric materials. Type II is composed of cylindrical rods of Nb enclosed with an interfacial layer and a background material of the same dielectric materials used in type I. With the calculated photonic band structures, it can be found that the PBG can be significantly enlarged using the ternary structures more than the conventional (binary) structures. In addition, the different distributions of the constituent materials of the ternary structures have a distinct effect on the width of the PBGs.