Conical dispersions induced interface states in two-dimensional photonic crystals

Abstract

In our previous work, we use accidental degeneracy to realize conical dispersions at Γ point (k = 0) in two-dimensional (2D) photonic crystals (PCs) [1]. The conical dispersion consists of a triply degenerate state with two linear bands touching at the Dirac-like point and an additional flat band intersecting it at the same frequency. If the conical dispersion is derived from monopole and dipole excitations, the system can be described as a zero-refractive-index material with effective permittivity and permeability equal to zero simultaneously at the Dirac-like point frequency. Generally speaking, there is no guarantee that interface states can be found at the boundary of 2D PCs. Recently, we found that if an interface is formed by two semi-infinite PCs with the system parameters slightly perturbed from the condition of conical dispersion formation, there are always interface states [2]. The conical dispersion guarantees the existence of gaps both below and above the Dirac-like point in the projected band structure, a necessary condition for the formation of interface states. Meanwhile, the quasi-longitudinal flat band in the conical dispersion ensures that these two gaps have different signs of surface impedances, which can be obtained by the layer-by-layer multiple scattering theory. Since there is a relationship between the sign of the surface impedance and the geometric phase of the bulk band, the existence of interface states can be also explained by the geometric phases of the bulk bands. The presence of interface states in such systems is verified by the microwave experiment [3].