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Register a new userObservation of Three-dimensional Photonic Dirac points and Spin-polarized Surface Arcs
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Topological phases arise from the elegant mathematical structures imposed by the interplay between symmetry and topology1-5. From gapped topological insulators to gapless semimetals, topological materials in both quantum and classical systems, have grown rapidly in the last decade. Among them, three-dimensional Dirac semimetal lies at the topological phase transition point between various topological phases. It shares multiple exotic topological features with other topological materials, such as Fermi arcs and chiral anomaly with Weyl semimetals30, spin-dependent surface states with topological insulators29. In spite of the important role it plays in topological physics, no experimental observation of three-dimension Dirac points has been reported in classical systems so far. Here, we experimentally demonstrate three-dimension photonic Dirac points in an elaborately designed photonic metamaterial, in which two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry31. Spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which paves the way towards spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics.
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Simulation of fermionic relativistic physics (such as Dirac and Weyl points) has led the dicovery of versatile and exotic phenomena in photonics, of which the optical-frequency realization is, however, still a challenging aim. Here we discover that the commonly-used woodpile photonic crystals for optical-frequency applications host novel fermionic relativistic degeneracies: a Dirac linenode and a topological quadratic degeneracy point, as {em guaranteed} by the nonsymmorphic crystalline symmetry. By reducing the space symmetry, type-II Dirac/Weyl points emerge as the descendants of the quadratic degeneracy point. These exotic optical waves mimicking the physics of unconventional fermionic relativistic waves and hosting anomalous optical properties in subwavelength, all-dielectric photonic crystals could open a new avenue for future optical science.
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Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display higher order Fermi arcs, which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher order Fermi arcs. When higher order Fermi arcs do exist, they obey either a $mathbb{Z}_2$ (four-fold rotation axis) or $mathbb{Z}_3$ (three- or six-fold rotation axis) group structure. Finally, we build two models with six-fold symmetry to illustrate the cases with and without higher order Fermi arcs. We predict higher order Fermi arcs in Na$_3$Bi.
A tetragonal photonic crystal composed of high-index pillars can exhibit a frequency-isolated accidental degeneracy at a high-symmetry point in the first Brillouin zone. A photonic band gap can be formed there by introducing a geometrical anisotropy in the pillars. In this gap, gapless surface/domain-wall states emerge under a certain condition. We analyze their physical property in terms of an effective hamiltonian, and a good agreement between the effective theory and numerical calculation is obtained.
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