Nonlinear Topological Valley Hall Edge States Arising from Type-II Dirac Cones

TL;DR

This paper demonstrates the existence of nonlinear valley Hall edge states in photonic lattices with type-II Dirac points, revealing topological gap quasi-solitons that differ from linear states and previous solitons, with potential applications in topological lasers.

Contribution

It introduces nonlinear topological valley Hall edge states in photonic systems with type-II Dirac points, a novel phenomenon not observed in prior linear or solitonic topological states.

Findings

Discovery of self-trapped topological gap quasi-solitons

Distinct behavior from linear topological states

Potential for advanced topological light sources

Abstract

Type-II Dirac/Weyl points, although impermissible in particle physics due to Lorentz covariance, were uncovered in condensed matter physics, driven by fundamental interest and intriguing applications of topological materials. Recently, there has been a surge of exploration of such generic points using various engineered platforms including photonic crystals, waveguide arrays, metasurfaces, magnetized plasma and polariton micropillars, aiming towards relativistic quantum emulation and understanding of exotic topological phenomena. Such endeavors, however, have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials. Here, we demonstrate nonlinear valley Hall edge states (VHESs) in laser-writing anisotropic photonic lattices hosting type-II Dirac points. These self-trapped VHESs, manifested as topological gap quasi-solitons, are fundamentally distinct from their linear counterparts in type-I lattices and from all previously found topological solitons. Our finding may provide a route for understanding nonlinear phenomena in Lorentz-violating topological systems and for developing advanced light sources from topological insulator lasers.