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 (27)

• Topological Insulators
• Berry Phase Effects on Electronic Properties
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Topological Photonics
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Valley contrasting physics in graphene: magnetic moment and topological transport
• 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
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• All-Si Valley-Hall Photonic Topological Insulator
• Quantum anomalous Hall effect and related topological electronic states
• Intrinsic spin Hall effect in platinum metal
• Valley-protected backscattering suppression in silicon photonic graphene
• Valley-contrasting orbital angular momentum in photonic valley crystals
• Experimental Observation of Three-Component 'New Fermions' in Topological Semimetal MoP
• Experimental Observation of Large Chern numbers in Photonic Crystals
• Triple Point Topological Metals
• Do Linear Dispersions of Classical Waves Mean Dirac Cones?
• Topological Semimetals with Triply Degenerate Nodal Points in θ-phase Tantalum Nitride
• Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study
• Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --
• The Emergence of Topological Nodal Points in Photonic Crystal with Mirror Symmetry
• High Chern number quantum anomalous Hall phases in graphene ribbons with Haldane orbital coupling
• Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Cited by in corpus (6)

• Topological photonic crystals: physics, designs and applications
• Hybrid topological photonic crystals
• Photonic topological phase transition induced by material phase transition
• Photonic Chern insulators made of gyromagnetic hyperbolic metamaterials
• Size and host-medium effects on topologically protected surface states in bi-anisotropic 3D optical waveguides
• Coexistent topological and chiral phonons in chiral RhGe: An ab initio study