Higher-order Dirac Semimetal in a Photonic Crystal

TL;DR

This paper reports the design and experimental demonstration of a three-dimensional photonic crystal that exhibits a higher-order Dirac semimetal phase, featuring topologically protected hinge states and advancing the understanding of higher-order topological semimetals.

Contribution

It introduces a realistic 3D photonic crystal model that realizes a higher-order Dirac semimetal phase with experimental microwave measurements.

Findings

Hosts two four-fold Dirac points

Displays higher-order hinge states connecting Dirac points

Characterized by  topological invariant

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 \chi(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.