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

October 20, 2020

Discovering and synthesizing symmetry-protected topological (SPT) band degeneracies, including nodal points and nodal lines (NLs), is a rapidly growing frontier in the field of topological materials. Interestingly, since the crystallographic space groups impose fewer constraints on the energy bands than the continuous Poincaré group, more exotic multifold band crossings were found in lattice systems, which have no counterparts in high-energy physics. 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. However, in dielectric PhCs, there are always two gapless bands emerging from the origin of light cone (ω=|k|=0), irrespective of the space group representations at that point. It was recently demonstrated that this intrinsic singularity of EM fields permits higher minimal connectivity for the lowest photonic bands than for their electronic counterparts without spin-orbit coupling and may further enforce unique photonic band crossings even in symmorphic lattices.

In a new paper published in Light Science & Application, a team of scientists, led by Professor C. T. Chan from the Hong Kong University of Science and Technology and Associate Professor Yuntian Chen from Huazhong University of Science and Technology, and co-workers have discovered a new kind of hidden symmetry in PhCs, due to the special characters of Maxwell equations. Based on this hidden symmetry, they found 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. More interestingly, the nexus points of three NLs behaver as a new kind of magnetic monopole terminating Berry flux strings in the momentum space, and show novel spin-1 canonical diffraction.

In general, the stationary Maxwell's equations can be written as a generalized eigenvalue problem . Since all space group transformations leave the curl matrix N ?(r) invariant, a PhC respects a space group symmetry A ? only if its constitutive tensor obeys A ??M ?(r)A ?^(-1)=M ?(r). However, a generic symmetry A ? of Maxwell's equations (1) operates on the Hamiltonian H ?(r)=M ?(r)^(-1) N ?(r) of EM fields, namely, requiring ?A H ?(r) A ?^(-1)=H ?(r), and not on N ?(r) and M ?(r) separately. This fact implies that the conventional space groups alone are insufficient to determine the symmetry properties as well as the band connectivities of photonic systems.

In this work, they proposed a simple layer-stacked photonic structure consisting of anisotropic dielectrics to exemplify such hidden symmetries of Maxwell's equations beyond space groups. They show that a hidden symmetry, more specifically, a generalized fractional screw rotation symmetry, together with time reversal symmetry guarantees the emergence of Kramers-like straight NLs passing through the Brillouin zone centre and results in unusual photonic band connectivities. Furthermore, they demonstrated the lowest Kramers-like NL can almost always intersect with two other SPT nodal rings at two triply degenerate nexus points (NPs), which can be seen as a new kind of magnetic monopole connecting Berry flux strings in momentum space. By breaking the hidden symmetry, the two NPs are lifted and type-II and type-III nodal rings are achieved in the PhC for the first time.

In addition, the peculiar anisotropic band structure near the NPs, especially the spin-1 conical dispersion of the iso-frequency surfaces, lead to novel transport phenomena.

Unlike the usual conical diffraction of light scattered at an ordinary linearly crossing point on the nodal lines characterized by spin-1/2 dynamics, , the diffraction at the triple NPs appears strikingly different spin-1 wave behavior described by a Schrödinger equation with the 2D spin-1 Hamiltonian. The authors showed that such unconventional spin-1 conical diffraction can be used to generate optical vortices with a maximum topological charge of 2.
-end-


Light Publishing Center, Changchun Institute of Optics, Fine Mechanics And Physics, Chinese Academy

Related Symmetry Articles from Brightsurf:

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals
The paper reveals that Maxwell's equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and paves the way to finding novel topological degeneracies unique in photonics.

Polarimetric parity-time-symmetric photonic system
Parity-time symmetry (PT), rooting in quantum field theory, are now shining in photonic systems.

Physicists discover new magnetoelectric effect
A special material was found, which shows a surprising new effect: Its electrical properties can be controlled with a magnetic field.

Squaring the circle -- Breaking the symmetry of a sphere to control the polarization of light
Scientists at Tokyo Institute of Technology (Tokyo Tech, Japan) and Institute of Photonic Sciences (ICFO, Spain) develop a method to generate circularly polarized light from the ultimate symmetrical structure: the sphere.

Topological superconducting phase protected by 1D local magnetic symmetries
Scientists from China and USA classified 1D gapped topological superconducting quantum wires with local magnetic symmetries (LMSs), in which the time-reversal symmetry is broken but its combinations with certain crystalline symmetries, such as MxT, C2zT, C4zT, and C6zT, are preserved.

Routing valley exciton emission of a WS2 monolayer via in-plane inversion-symmetry broken PhC slabs
The researchers demonstrate all-dielectric photonic crystal (PhC) slabs without in-plane inversion symmetry (C2 symmetry) could separate and route valley exciton emission of a WS2 monolayer at room temperature.

How does spatial multi-scaled chimera state produce the diversity of brain rhythms?
This work revealed that the real brain network has a new chimera state -- spatial multi-scaled chimera state, and its formation is closely related the local symmetry of connections.

The tug-of-war at the heart of cellular symmetry
Researchers develop an artificial cell that brings to light the dynamics that govern each cell's internal symmetry.

Counterintuitive phase behavior observed in isotopic hydrogen (H2-HD-D2) alloy
A joint team from the Institute of Solid State Physics of the Hefei Institutes of Physical Science, collaborating with researchers from the Center for High Pressure Science & Technology Advanced Research and University of Edinburgh, has reported a new discovery in which they found counterintuitive effects of isotopic doping on the phase diagram of H2-HD-D2 molecular alloy.

Oriented hexagonal boron nitride foster new type of information carrier
Present computers use the presence or absence of charge (0s and 1s) to encode information, where the physical motion of charges consume energy and causes heat.

Read More: Symmetry News and Symmetry Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.