Type-II Dirac points and topological Fermi arcs in nonlocal metamaterials

Abstract

Dirac semimetals are topological materials with degenerated Dirac points in their band structures. In particular, the Dirac points play a central role in the topologically protected phases. Recently, it was reported that the peculiar type-II Dirac points could be realized in photonics by means of photonic crystals (PCs). Nevertheless, the practical implementation is rather challenging. In this paper, we demonstrate that the nonlocal effect in the interior of a homogeneous photonic metamaterial (HPM) enables the existence of type-II Dirac points in the HPM's band structure. With theoretical formulations and numerical evaluations, we discuss the evolution of the HPM's band type and present the interesting transition between type-I and type-II Dirac degeneracy of the HPMs. Remarkably, a pair of the type-II Dirac points can be generated at two different frequencies, which is supported by the mode overlapping in the HPMs with weak nonlocality. The Fermi arc surface states connect the projections of the type-II Dirac points at the boundary between the vacuum and HPMs. The topological protection of the Fermi arc surface states is verified by the reflectionless transmission with sharp corners. Our paper provides a fundamental understanding of topological photonics by type-II Dirac points in HPMs.