Double Dirac Cones and Topologically Non-Trivial Phonons for Continuous, Square Symmetric (C${}_{4v}$ and C${}_{2v}$) Unit Cells

Abstract

Because phononic topological insulators have primarily been studied in discrete, graphene-like structures with C${}_6$ or C${}_3$ hexagonal symmetry, an open question is how to systematically achieve double Dirac cones and topologically non-trivial structures using continuous, non-hexagonal unit cells. Here, we address this challenge by presenting a novel computational methodology for the inverse design of continuous two-dimensional square phononic metamaterials exhibiting C${}_{4v}$ and C${}_{2v}$ symmetry. This leads to the systematic design of square unit cell topologies exhibiting a double Dirac degeneracy, which enables topologically-protected interface propagation based on the quantum spin Hall effect (QSHE). Numerical simulations prove that helical edge states emerge at the interface between two topologically distinct square phononic metamaterials, which opens the possibility of QSHE-based pseudospin-dependent transport beyond hexagonal lattices.

References in corpus (30)

• Topological Insulators
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Photonics
• Scheme to Achieve Silicon Topological Photonics
• Topological Acoustics
• Acoustic topological insulator and robust one-way sound transport
• The quantum spin Hall effect and topological insulators
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological mechanics of gyroscopic metamaterials
• Topologically protected elastic waves in phononic metamaterials
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Classification of topological phonons in linear mechanical metamaterials
• Experimental realization of on-chip topological nanoelectromechanical metamaterials
• Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides
• Observation of topologically protected helical edge modes in Kagome elastic plates
• Design and Experimental Observation of Valley-Hall Edge States in Diatomic-Graphene-like Elastic Waveguides
• Topological Insulators by Topology Optimization
• Helical edge states and topological phase transitions in phononic systems using bi-layered lattices
• Room Temperature Quantum Spin Hall Insulators with a Buckled Square Lattice
• Self-ordering induces multiple topological transitions for elastic waves in phononic crystals
• Observation of topological edge states of sound at a momentum away from the high-symmetry point
• Dirac cones beyond the honeycomb lattice: a symmetry based approach
• Dial-in Topological Metamaterials Based on Bistable Stewart Platform
• Electrically Tunable Conductance and Edge Modes in Topological Crystalline Insulator Thin Films: Tight-Binding Model Analysis
• The Nature of Topological Protection in Spin and Valley Hall Insulators
• Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
• Edge states and corner modes in second-order topological phononic crystal plates

Cited by in corpus (2)

• Customizing pseudospin unidirectional states of acoustic and electromagnetic waves in two-dimensional phoxonic topological insulators via multi-objective strategies
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium