Zero Refractive Index Properties of Two-Dimensional Photonic Crystals with Dirac Cones

The zero refractive index properties of two-dimensional photonic crystals (PCs) are studied theoretically. Three necessary conditions for PCs to mimic the zero index materials (ZIMs) are obtained. In addition, through a comparative study of the properties for two representative PC structures with different types of Dirac cones, we find that the PC with a Dirac-like cone which meets the three necessary conditions does not behave as a ZIM in some cases. Further analysis shows that its non-zero index properties originate from the flat dispersion band. These findings clarify the fundamental physical issue of which type of Dirac cone PC can mimic a real ZIM.