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

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.

Double-bowl state in photonic Dirac nodal line semimetal

“…The topological classification of the photonic systems was originally thought to be a trivial extension of the electronic counterpart and described by spinless space groups. However, detailed analyses reveal that photonic systems are distinct from the electronic counterparts, and connectivity at zero frequency in dielectric materials and hidden symmetry enforced nexus points are latter found to be unique to photonic systems 12,13 . Here in this work, we provide a stringent photonic realization of Dirac nodal line semimetal (DNLS) which is not a spinless version of the electronic DNLS.…”

Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals

“…1(d). For the intrinsic symmetry of electromagnetism in the anisotropic permittivity [23],the M y -even (with only (E x , E z , H y )) and M y -odd (with only (H x , H z , E y )) states with respect to the k y =0 mirror plane are then found in this photonic crystal when θ = 0 • , as denoted by the blue and red bands in FIG. 1(d).…”

“…Specifially, Dirac/Weyl semimetals have been demonstrated to exhibit several peculiar phenomena, such as Fermi arcs and chiral anomaly [1,11], while for type-II Weyl points, the unique features including tilted cone dispersion and the surface states existed in an incomplete bandgap would bring more exotic effects [10]. In classical systems, the analogues of various topological semimetals have also been achieved in photonics [12][13][14][15][16][17][18][19][20][21][22][23][24][25], acoustics [26][27][28][29][30][31],circuits [32] and magnetic systems [33,34]. Type-I Weyl points and the arc surface states have been theoretically [12] and experimentally [13,14,27] verified in 3D photonic/phononic crystals and metamaterials, and also been found recently that the Weyl semimetals can sustain higher-order topological hinge states [35][36][37][38].…”

Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems

“…Another example of crystallographic symmetry mediated optical response of meta-atoms was demonstrated in the discovery of hourglass nodal lines in a photonic metamaterial [23]. Although it may seem that band topologies can be solely determined by global crystallographic symmetries, the interplay between them and local optical responses is surprisingly rich in new physics, for instance, the hidden symmetries that are unforeseen by crystallographic group theory [160]. It is, however, worth noting that without exquisite design, the touching point between equi-frequency contours in natural biaxial crystal forms a 3-dimensional nodal chain if the bands at higher momentum are considered cut off and flattened by the Brillouin zone boundary (Figure 5c).…”