Higher-order Dirac Semimetal in a Photonic Crystal

Abstract

The recent discovery of higher-order topology has largely enriched the classification of topological materials. Theoretical and experimental studies have unveiled various higher-order topological insulators that exhibit topologically protected corner or hinge states. More recently, higher-order topology has been introduced to topological semimetals. Thus far, realistic models and experimental verifications on higher-order topological semimetals are still very limited. Here, we design and demonstrate a three-dimensional photonic crystal that realizes a higher-order Dirac semimetal phase. Numerical results on the band structure show that the designed three-dimensional photonic crystal is able to host two four-fold Dirac points, the momentum-space projections of which at an edge are connected by higher-order hinge states. The higher-order topology can be characterised with the calculation of the χ(6) topological invariant at different values of k_z. An experiment at microwave frequencies is also presented to measure the hinge state dispersion. Our work demonstrates the physical realization of a higher-order Dirac semimetal phase and paves the way to exploring higher-order topological semimetals phases in three-dimensional photonic systems.

References in corpus (9)

• Topological Photonics
• Scheme to Achieve Silicon Topological Photonics
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological Semimetals
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals

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• Two-Dimensional Higher-Order Topological Metals
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs