Manipulation of Dirac Cones in Mechanical Graphene

Abstract

Mechanical graphene, which is a spring-mass model with the honeycomb structure, is investigated. The vibration spectrum is dramatically changed by controlling only one parameter, spring tension at equilibrium. In the spectrum, there always exist Dirac cones at K- and K'-points. As the tension is modified, extra Dirac cones are created and annihilated in pairs. When the time reversal symmetry is broken by uniform rotation of the system, creation and annihilation of the Dirac cones result in a jump of the appropriately defined Chern number. Then, a flip of the propagation direction of the chiral edge modes takes place, which gives an experimental way to detect the topological transition. This is a bulk-edge correspondence of the classical system. We also demonstrate the other important concept, symmetry protection of the topological states, is at work in the classical system. For the time reversal invariant case, the topological edge modes exist for the fixed boundary condition but not for the free boundary condition. This contrast originates from the symmetry breaking at the free boundary.

arXiv comment7 figures

References in corpus (37)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators with Inversion Symmetry
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Imaging topological edge states in silicon photonics
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• High-accuracy first-principles determination of the structural, vibrational and thermodynamical properties of diamond, graphite, and derivatives
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Spawning rings of exceptional points out of Dirac cones
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• The Zak phase and the existence of edge states in graphene
• Artificial graphene as a tunable Dirac material
• The phonon dispersion of graphite revisited
• Topological phonon modes and their role in dynamic instability of microtubules
• Optomechanically induced non-reciprocity in microring resonators
• Nonlinear conduction via solitons in a topological mechanical insulator
• Extremal transmission at the Dirac point of a photonic band structure
• Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --
• Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene
• A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal
• Coriolis Force Induced Quantum Hall Effect for Phonons
• Vibrational Tamm states at the edges of graphene nanoribbons
• Bulk-edge correspondence in graphene with/without magnetic field: Chiral symmetry, Dirac fermions and Edge states
• Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices
• Optomechanical Dirac Physics
• Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions: Application to Fermionic Shastry-Sutherland Model
• Topological phonon modes in filamentous structures
• A simple model for the vibrational modes in honeycomb lattices
• Mechanism of phonon localized edge modes

Cited by in corpus (92)

• Non-Hermitian Physics
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Classification of topological phonons in linear mechanical metamaterials
• Artificial gauge fields in materials and engineered systems
• Topological waves in fluids with odd viscosity
• Topological Phase Transition in Mechanical Honeycomb Lattice
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Model for Topological Phononics and Phonon Diode
• Pseudospins and topological effects of phonons in a Kekule lattice
• Pseudomagnetic fields for sound at the nanoscale
• Snowflake Topological Insulator for Sound Waves
• Helical edge states and topological phase transitions in phononic systems using bi-layered lattices
• Mirror skin effect and its electric circuit simulation
• Exceptional rings protected by emergent symmetry for mechanical systems
• Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
• Experimental demonstration of topological waveguiding in elastic plates with local resonators
• Topological nodal states in circuit lattice
• Experimental Realization of a Reconfigurable Electroacoustic Topological Insulator
• Topological networks for quantum communication between distant qubits
• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• Soft self-assembly of Weyl materials for light and sound
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• van der Waals metamaterials
• Acoustic twisted bilayer graphene
• Bulk-edge correspondence in topological pumping
• Topological Edge Modes by Smart Patterning
• Bulk-edge correspondence of classical diffusion phenomena
• Square-root topological semimetals
• L lines, C points and Chern numbers: understanding band structure topology using polarization fields
• Interfacial waveforms in chiral lattices with gyroscopic spinners
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Topologically protected elastic waves in one-dimensional phononic crystals of continuous media
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
• Topologically protected pseudospins in 2D spring-mass system
• Phonon rotoelectric effect
• Topological continuum charges of acoustic phonons in 2D
• Mechanical Graphene
• Higher-order topological insulators in a magnetic field
• Elastic Temporal Waveguiding
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Phononic topological insulators with tunable pseudospin physics
• Non-Hermitian topology in rock-paper-scissors games
• Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping
• Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
• Fragile phonon topology on the honeycomb lattice with time-reversal symmetry
• Spin-orbit coupling in a hexagonal ring of pendula
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Design of GaAs-based valley phononic crystals with multiple complete phononic bandgaps at ultra-high frequency
• Edge states of mechanical diamond and its topological origin
• Duality of Topological Edge States in a Mechanical Kitaev Chain
• Strain topological metamaterials
• Weyl points of mechanical diamond
• Universal features of canonical phonon angular momentum without time-reversal symmetry
• Higher-order topological heat conduction on a lattice for detection of corner states
• Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
• Topological sound in active-liquid metamaterials
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Granular Graphene: direct observation of zigzag and armchair edge waves
• Abnormal Phonon Angular Momentum due to Off-diagonal Elements in Density Matrix induced by Temperature Gradient
• On E-Discretization of Tori of Compact Simple Lie Groups: II
• Topological band structure of surface acoustic waves on a periodically corrugated surface
• Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models
• Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Observation of Multiple Topological Corner States in Thermal Diffusion
• Topological obstructed atomic limit by annihilating Dirac fermions
• Elastic Spin Hall effect in Mechanical Graphene
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Spontaneously-Induced Dirac Boundary State and Digitization in a Nonlinear Resonator Chain
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Complete absorption of topologically protected waves
• Hierarchical Topological States in Thermal Diffusive Networks
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Characterization of elastic topological states using dynamic mode decomposition
• The effects of dissipation on topological mechanical systems
• Topological Micro-Electro-Mechanical Systems
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Selective branching, quenching, and converting of topological modes
• Chiral topological phases in designed mechanical networks
• Inelastic Neutron Scattering for Direct Detection of Chiral Phonons
• Zero-frequency corner modes in mechanical graphene
• SAW interdigitated transducers as topological mechanical metamaterial
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices