Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry

TL;DR

This paper demonstrates the coexistence and interaction of pseudospin- and valley-Hall-like edge states in a $C_{3v}$ symmetric photonic crystal, enabling advanced control of electromagnetic wave routing for multifunctional applications.

Contribution

It introduces a novel photonic crystal design supporting simultaneous pseudospin and valley topological states, and demonstrates their combined manipulation for wave routing.

Findings

Three complete topological band gaps were created with different origins.

Tri-band pseudospin- and valley-momentum locking edge states were supported.

Unidirectional wave routing can be selectively controlled by pseudospin and valley degrees of freedom.

Abstract

We demonstrate the coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry, which is composed of three interlacing triangular sublattices with the same lattice constants. By tuning the geometry of the sublattices, three complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at the $\Gamma$ point and the other two due to the gapping out of Dirac cones associated with the valley degree of freedom at the $K, K'$ points. The system can support tri-band pseudospin- and valley-momentum locking edge states at properly designed domain-wall interfaces. Furthermore, to demonstrate the novel interplay of the two kinds of edge states in a single configuration, we design a four-channel system, where the unidirectional routing of electromagnetic waves against sharp bends between two routes can be selectively controlled by the pseudospin and valley degrees of freedom. Our work combines the pseudospin and valley degrees of freedom in a single configuration and may provide more flexibility in manipulating electromagnetic waves with promising potential for multiband and multifunctional applications.