Tuning Topological Phase Transitions in Hexagonal Photonic Lattices Made of Triangular Rods

Abstract

In this paper, we study topological phases in a 2D photonic crystal with broken time ($\mathcal{T}$) and parity ($\mathcal{P}$) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks $\mathcal{T}$ symmetry while the triangular rods breaks $\mathcal{P}$ symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases with different gap Chern numbers ($C_g$) including $|C_g|>1$ as well as quantum valley Hall (QVH) phases with contrasting valley Chern numbers ($C_v$), depending on the orientation of the triangular rods. Furthermore, phase transitions among these topological phases, such as from QAH to QVH and vice versa, can be engineered by a simple rotation of the rods. Our band theoretical analyses reveal that the Dirac nodes at the $K$ and $K^{\prime }$ valleys in the momentum space are produced and protected by the mirror symmetry ($m_y$) instead of the $\mathcal{P}$ symmetry, and they become gapped when either $\mathcal{T}$ or $m_y$ symmetry is broken, resulting in a QAH or QVH phase, respectively. Moreover, a high Chern number ($C_g=-2$) QAH phase is generated by gapping triply degenerate nodal points rather than pairs of Dirac points by breaking $\mathcal{T}$ symmetry. Our proposed photonic crystal thus provides a platform for investigating intriguing topological phenomena which may be challenging to realize in electronic systems, and also has promising potentials for device applications in photonics such as reflection-free one-way waveguides and topological photonic circuits.

References in corpus (8)

• Topological Photonics
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• The Valley Hall Effect in MoS2 Transistors
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Analogs of quantum Hall effect edge states in photonic crystals
• Do Linear Dispersions of Classical Waves Mean Dirac Cones?
• Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study
• The Emergence of Topological Nodal Points in Photonic Crystal with Mirror Symmetry