Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices

Abstract

The exceptional properties exhibited by two-dimensional materials, such as graphene, are rooted in the underlying physics of the relativistic Dirac equation that describes the low energy excitations of such molecular systems. In this study, we explore a periodic lattice that provides access to the full solution spectrum of the extended Dirac Hamiltonian. Employing its photonic implementation of evanescently coupled waveguides, we indicate its ability to independently perturb the symmetries of the discrete model (breaking, also, the barrier towards the type-II phase) and arbitrarily define the location, anisotropy, and tilt of Dirac cones in the bulk. This unique aspect of topological control gives rise to highly versatile edge states, including an unusual class that emerges from the type-II degeneracies residing in the complex space of k. By probing these states, we investigate the topological nature of tilt and shed light on novel transport dynamics supported by Dirac configurations in two dimensions.

Type-II Dirac photonic lattices

“…Note added: A paper [59] on constructing type-II Dirac points by proposing a band-folding scheme, and a paper [60] on symmetry-controlled edge states in the type-II phase of Dirac photonic lattices, were published after submission of this paper. We would like to emphasize that, in our work for the first time, we find the simplest way to construct type-II Dirac points which only depends on the spatial geometry of the photonic lattice.…”

Photonic circuits written by femtosecond laser in glass: improved fabrication and recent progress in photonic devices

“…[125][126][127] WG photonic lattices are frequently adopted to build photonic topological structures for investigating the interplay of topology and interparticle interactions. [128][129][130][131] For example, the helicity of the evanescently coupled helical WG array would break the z-reversal symmetry in a honeycomb photonic lattice [Figs. 10(a) and 10(b)], which leads to formation of Floquet topological insulators, and topologically protected transport of visible light is observed on the lattice edges.…”

Nonlinear topological valley Hall edge states arising from type-II Dirac cones

“…Different from type-I Dirac cones in graphene where the corresponding Fermi surface is a point, there are also so-called tilted type-II Dirac cones with the Fermi surface being a pair of crossing lines. [53][54][55][56][57][58][59][60][61][62][63][64] Type-II Dirac cones violate the Lorentz symmetry, thus allowing for quasi-particle-mediated phenomena that do not exist in high-energy physics analogically investigated in condensed matter physics. In photonics, for example, type-II Dirac cones are expected to bring new features due to their nonisotropic transport properties arising from the distinctive dispersions.…”

“…In photonics, for example, type-II Dirac cones are expected to bring new features due to their nonisotropic transport properties arising from the distinctive dispersions. Photonic lattices can be readily designed to possess such Dirac cones, 54,57 making them attractive for investigation of nontrivial topological phenomena. 61 In this work, as one typical example, we propose and demonstrate experimentally a scheme to establish type-II Dirac photonic lattices in a nonlinear medium and, more importantly, to reveal the existence of topologically protected nonlinear VHE states.…”