Line nodes, Dirac points, and Lifshitz transition in two-dimensional nonsymmorphic photonic crystals

Abstract

Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple two-dimensional photonic crystal lattices with gap closures, i.e., band degeneracies protected by nonsymmorphic symmetry. Our photonic structures are relatively easy to fabricate, consisting of two inequivalent dielectric cylinders per unit cell. Along high-symmetry directions, they exhibit line degeneracies protected by glide-reflection symmetry and time-reversal symmetry, which we explicitly demonstrate for $pg,pmg,pgg$, and $p4g$ nonsymmorphic groups. They also exhibit point degeneracies (Dirac points) protected by a ${Z}_{2}$ topological number associated only with crystalline symmetry. Strikingly, the robust protection of $pg$ symmetry allows a Lifshitz transition to a type-II Dirac cone across a wide range of experimentally accessible parameters, thus providing a convenient route for realizing anomalous refraction. Further potential applications include a stoplight device based on electrically induced strain that dynamically switches the lattice symmetry from $pgg$ to the higher $p4g$ symmetry. This controls the coalescence of Dirac points and hence the group velocity within the crystal.