P T-symmetric photonic lattices with type-II Dirac cones

Abstract

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons and, more specifically, for mimicking the Klein tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the PT-symmetric photonic lattices with type-II Dirac cones for the first time to our knowledge. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the PT symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with PT symmetry only decays because of diffraction, whereas in the PT symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.