The unusual surface plasmon modes and switching bandgap of three-dimensional (3D) photonic crystals (PCs) with pyrochlore lattices that are composed of core isotropic positive-index dielectric spheres surrounded by epsilon-negative (ENG) material shells inserted in the air are theoretically investigated in detail based on the plane wave expansion method. Numerical simulations show that the proposed double-shell structure can obtain complete photonic band gaps (PBGs) and a flatbands region. Compared to the conventional lattices, such as diamond, face-centered-cubic, body-centered-cubic, and simple-cubic lattices, a larger PBG can be achieved in the pyrochlore arrangement. It is noticed that the flatbands region is determined by the existence of surface plasmon modes. If the thickness of the ENG material shell is larger than a threshold value, the band structures of such 3D PCs will be similar to those obtained from the same structure containing pure ENG material spheres. In this case, the inserted core spheres will also not affect the band structures. It is also provided that the upper edge of the flatbands region does not depend on the topology of the lattice. Our results also demonstrate that the PBG can be manipulated by the radius of the core dielectric sphere, the dielectric constant of ENG materials, and the electronic plasma frequency, respectively. This means that the PBG can be obtained by replacing the pure ENG material spheres with such double-shell structures to save the material in the realization. Thus, such proposed 3D PCs offer a novel way to realize the potential applications.
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