Symmetry-protected topological photonic crystal in three dimensions

Abstract

Topology of electron wavefunctions was first introduced to characterize the quantum Hall states in two dimensions discovered in 1980 (ref.). Over the past decade, it has been recognized that symmetry plays a crucial role in the classification of topological phases, leading to the broad notion of symmetry-protected topological phases. As a primary example, topological insulators are distinguished from normal insulators in the presence of time-reversal symmetry (τ). A three-dimensional (3D) topological insulator exhibits an odd number of protected surface Dirac cones, a unique property that cannot be realized in any 2D systems. Importantly, the existence of topological insulators requires Kramers' degeneracy in spin-orbit coupled electronic materials; this forbids any direct analogue in boson systems. In this report, we discover a 3D topological photonic crystal phase hosting a single surface Dirac cone, which is protected by a crystal symmetry - the nonsymmorphic glide reflection rather than τ. Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D 'generalized Dirac points' discovered in the bulk of our crystal. The Z 2 bulk invariant is characterized through the evolution of Wannier centres. Our proposal - readily realizable using ferrimagnetic materials at microwave frequencies - expands the scope of 3D topological materials from fermions to bosons.