Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

Zhongfei Xiong,Yuntian Chen,C T Chan,Ruo-Yang Zhang,Rui Yu

doi:10.1038/s41377-020-00382-9

Abstract

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations. The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

Highlights

We show that a hidden symmetry, a generalized fractional screw rotation symmetry, together with time reversal symmetry guarantees the emergence of Kramers-like straight nodal lines (NLs) passing through the Brillouin zone (BZ) centre and results in unusual photonic band connectivities
photonic crystals (PhCs) manifests a hidden symmetry of Maxwell’s equations, which directly influences the connectivity of photonic bands and engenders a pair of triply degenerate nexus points (NPs) where three symmetry-enforced NLs intersect
The hidden symmetry here stems from the fractional periods of different components of εr, which reflects a geometric property of the PhC but cannot be described by the conventional space groups

Summary

Introduction

Discovering and synthesizing symmetry-protected topological (SPT) band degeneracies, including nodal points[1,2,3,4,5,6,7,8,9,10,11,12,13] and nodal lines (NLs)[14,15,16,17,18,19,20,21,22,23,24,25], is a rapidly growing frontier in the field of topological materials. In PhCs, the topology of band structures is usually thought to be adequately described by spinless space groups, provided that special internal symmetries, such as electromagnetic (EM) duality, are not imposed on the EM materials. In dielectric PhCs, there are always two gapless bands emerging from zero frequency and momentum, ω 1⁄4 jkj 1⁄4 0, irrespective of the space group representations at that point. Watanabe and Lu recently revealed that this intrinsic singularity of EM fields permits higher minimal connectivity for the lowest photonic bands than for their electronic counterparts without

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Conclusion