Type-II Dirac point and extreme dispersion in one-dimensional plasmonic-dielectric crystals with off-axis propagation

Dirac cones exhibit linear crossing dispersion, which results in extraordinary topological properties in the energy bands. When the dispersion around the Dirac points is tilted, type-II or type-III Dirac points are present, which lead to intriguing transport phenomena. With the off-axis wave vector, a two-dimensional (2D) momentum space for one-dimensional (1D) crystals can be constructed. In this work, we revealed that the band structure in the extended 2D momentum space of carefully designed 1D plasmonic-dielectric crystals can be tuned to be highly tilted, forming type-II Dirac cones. In particular, an approximately upright dispersion can be achieved, which is referred to as a class-II Dirac point. Gapless interface states occur across the interface between two connected lattices formed by two distinct inversion-symmetry-broken crystals (i.e., type A and type B). The tilt of the band structure has a crucial influence on the formation of interface states and their sensitivity to the period, which results from the extraordinary properties of the surface impedance in the bulk gap. More importantly, class-II Dirac points exhibit peculiar topological properties. The wavelength area is divided into two regions, each of which can only support interface states for one configuration, type-AB or type-BA connections. Our results show that type-II Dirac points, especially those that are class II, have an underlying impact on the surface impedance and determine the existence of interface states.