Valley Chern Numbers and Boundary Modes in Gapped Bilayer Graphene

Abstract

Electronic states at domain walls in bilayer graphene are studied by analyzing their four and two band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures which occur in the bulk Hamiltonian parameter space. The important role played by intervalley coupling effects not directly captured by the continuum model is addressed using lattice calculations for specific domain wall structures.

6 pages, 7 figures

References in corpus (13)

• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Gate-induced insulating state in bilayer graphene devices
• Strain Solitons and Topological Defects in Bilayer Graphene
• Topological confinement in bilayer graphene
• Band Structure of ABC-Stacked Graphene Trilayers
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Electronic Highways in Bilayer Graphene
• Valley-Hall Kink and Edge States in Multilayer Graphene
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Transport studies of dual-gated ABC and ABA trilayer graphene: band gap opening and band structure tuning in very large perpendicular electric field
• Topological kink states at a tilt boundary in gated multi-layer graphene
• Marginality of bulk-edge correspondence for single-valley Hamiltonians

Cited by in corpus (207)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Observation of topological valley transport of sound in sonic crystals
• Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene
• Strain Solitons and Topological Defects in Bilayer Graphene
• Topologically-protected refraction of robust kink states in valley photonic crystals
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Electronic properties of graphene-based bilayer systems
• Direct Observation of Valley-polarized Topological Edge States in Designer Surface Plasmon Crystals
• Monolayer Topological Insulators: Silicene, Germanene and Stanene
• Photonic crystals for nano-light in moiré graphene superlattices
• Irradiated graphene as a tunable Floquet topological insulator
• Topological Sound
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Observation of topological valley modes in an elastic hexagonal lattice
• Valley Topological Phases in Bilayer Sonic Crystals
• Topologically Protected Helical States in Minimally Twisted Bilayer Graphene
• Gate-controlled topological conducting channels in bilayer graphene
• Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides
• Direct imaging of topological edge states at a bilayer graphene domain wall
• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Band structure and topological property of twisted double bilayer graphenes
• Topological Phase Transition in Mechanical Honeycomb Lattice
• Pseudospin-valley coupled edge states in a photonic topological insulator
• Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moiré Superlattices
• A valley valve and electron beam splitter
• Helical networks in twisted bilayer graphene under interlayer bias
• Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides
• Transport through a network of topological states in twisted bilayer graphene
• Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve and universal reversible logic gate
• Observation of Acoustic Valley Vortex States and Valley-Chirality Locked Beam Splitting
• Nanoscale Strain Engineering of Giant Pseudo-Magnetic Fields, Valley Polarization and Topological Channels in Graphene
• Spatially resolved edge currents and guided-wave electronic states in graphene
• Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers
• Scattering-Free Optical Edge States between Heterogeneous Photonic Topological Insulators
• Helical Network Model for Twisted Bilayer Graphene
• Electron quantum metamaterials in van der Waals heterostructures
• Electric Field Control of Soliton Motion and Stacking in Trilayer Graphene
• Intrinsic valley Hall transport in atomically thin MoS2
• Stacking Domain Wall Magnons in Twisted van der Waals Magnets
• Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene
• Peculiar electronic states, symmetries and Berry phases in irradiated $\alpha$-$T_3$ materials
• Tunable and giant valley-selective Hall effect in gapped bilayer graphene
• Stacking boundaries and transport in bilayer graphene
• Theory and Experimental Investigation of the Quantum Valley Hall Effect
• Band Topology, Orbital Phase Winding, and Selection Rules in Excitonic Physics in Two Dimensions
• Experimental Realization of a Reconfigurable Electroacoustic Topological Insulator
• Gapped Topological Kink States and Topological Corner States in Graphene
• Experimental evidence of robust acoustic valley Hall edge states in a non-resonant topological elastic waveguide
• Perfect Valley Filter in Topological Domain Wall
• Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals
• Electronic transmission through AB-BA domain boundary in bilayer graphene
• Plasmon reflections by topological electronic boundaries in bilayer graphene
• Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene
• Observation of topological edge states of sound at a momentum away from the high-symmetry point
• van der Waals Heterostructures of Germanene, Stanene and Silicene with Hexagonal Boron Nitride and Their Topological Domain Walls
• Manipulation and Characterization of the Valley Polarized Topological Kink States in Graphene Based Interferometers
• Quantum Spin-Valley Hall Kink States: From Concept to Materials Design
• Topological protection of multiparticle dissipative transport
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• DC conductivity of twisted bilayer graphene: Angle-dependent transport properties and effects of disorder
• Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene
• Perfect one-dimensional chiral states in biased twisted bilayer graphene
• Valley-projected edge modes observed in underwater sonic crystals
• Quantum Valley Hall Effect and Perfect Valley Filter Based on Photonic Analogs of Transitional Metal Dichalcogenides
• Visualizing the Effect of an Electrostatic Gate with Angle-Resolved Photoemission Spectroscopy
• Elastic Valley Spin Controlled Chiral Coupling in Topological Valley Phononic Crystals
• Valley Hall phases in Kagome lattices
• Ideal type-II Weyl phase and topological transition in phononic crystals
• Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene
• The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene
• The valley filter efficiency of monolayer graphene and bilayer graphene line defect model
• ${\mathbb{Z}}_2$ topological insulator analog for vortices in an interacting bosonic quantum fluid
• Aharonov-Bohm Oscillations in Minimally Twisted Bilayer Graphene
• Chiral zigzag modes and flatbands in network models of twisted bilayer graphene
• Valley and spin pump by scattering at non-magnetic disorders
• Self-organized pseudo-graphene on grain boundaries in topological band insulators
• Observation of boundary induced chiral anomaly bulk states and their transport properties
• Symmetry Protected Topological Charge in Symmetry Broken Phase: Spin-Chern, Spin-Valley-Chern and Mirror-Chern Numbers
• Tracking valley topology with synthetic Weyl paths
• Bound States in the Continuum in Bilayer Photonic Crystal with TE-TM Cross-Coupling
• Twistronics in graphene-based van der Waals structures
• High-Temperature Quantum Valley Hall Effect with Quantized Resistance and a Topological Switch
• A Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom
• Valley Anisotropy in Elastic Metamaterials
• Intrinsic Superflat Bands in General Twisted Bilayer Systems
• Topologically confined states at corrugations of gated bilayer graphene
• Spin-Valley Polarized Quantum Anomalous Hall Effect and a Valley-Controlled Half Metal in Bilayer Graphene
• Plasmonic Dirac Cone in Twisted Bilayer Graphene
• Floquet Valley-Polarized Quantum Anomalous Hall State in Nonmagnetic Heterobilayers
• Controlling the layer localization of gapless states in bilayer graphene with a gate voltage
• Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
• Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene
• Spontaneous Layer-Pseudospin Domain Walls in Bilayer Graphene
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Atomic-scale defects restricting structural superlubricity: Ab initio study study on the example of the twisted graphene bilayer
• Guiding Robust Valley-dependent Edge States by Surface Acoustic Waves
• Valley protected one-dimensional states in small-angle twisted bilayer graphene
• Dynamics of Symmetry-Breaking Stacking Boundaries in Bilayer MoS2
• Antiferromagnetic spin valve from heterostructure of two-dimensional hexagonal crystals
• Current partition at zero-line intersection of quantum anomalous Hall topologies
• Zero-line modes at stacking faulted domain walls in multilayer graphene
• Synthetic Kramers pair in phononic elastic plates and helical edge states on a dislocation interface
• Metallic Network of Topological Domain Walls
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• Giant atomic swirl in graphene bilayers with biaxial heterostrain
• Long-lived domain wall plasmons in gapped bilayer graphene
• The role of geometry and topological defects in the 1D zero-line modes of graphene
• Valley-based Cooper Pair Splitting via Topologically Confined Channels in Bilayer Graphene
• Correlated states of a triangular net of coupled quantum wires: Implications for the phase diagram of marginally twisted bilayer graphene
• Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain
• Chiral channel network from magnetization textures in 2D MnBi2Te4
• Quantum Valley Hall effect without Berry curvature
• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Time-reversal symmetric topological metal
• Tunable interband and intraband plasmons in twisted double bilayer graphene
• Topological valleytronics: Brought to light
• Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study
• Topological valley transport at the curved boundary of a folded bilayer graphene
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene
• Two phases with different domain wall networks and a reentrant phase transition in bilayer graphene under strain
• Floquet High Chern Insulators in Periodically Driven Chirally Stacked Multilayer Graphene
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Topological valley crystals in a photonic Su-Schrieffer-Heeger (SSH) variant
• Layer Zero-Line Modes in Antiferromagnetic Topological Insulators
• Charge density wave and finite-temperature transport in minimally twisted bilayer graphene
• Valley-Selective Topological Ordered States in Irradiated Bilayer Graphene
• Atomic configuration controlled photocurrent in van der Waals homostructures
• Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching
• Nonlinear response of biased bilayer graphene at terahertz frequencies
• Interplay between topological protected valley and quantum Hall edge transport
• Universal description of potential energy surface of interlayer interaction in two-dimensional materials by first spatial Fourier harmonics
• Transport Induced Dimer State from Topological Corner States
• Valley-selective Klein tunneling through superlattice barrier in graphene
• Stacking Textures and Singularities in Bilayer Graphene
• Substrate-induced topological minibands in graphene
• Marginally Self-Averaging One-Dimensional Localization in Bilayer Graphene
• Topological Valley Transport in Bilayer Graphene Induced by Interlayer Sliding
• Valley-polarized domain wall magnons in 2D ferromagnetic bilayers
• Kagomé network of chiral miniband-edge states in double-aligned graphene-hexagonal boron nitride structures
• Spontaneous Layer Polarization and Conducting Domain Walls in the Quantum Hall Regime of Bilayer Graphene
• Electrically tunable correlated domain wall network in twisted bilayer graphene
• Ferroelectric valley valves with graphene/MoTe${}_2$ van der Waals heterostructures
• Effective Floquet model for minimally twisted bilayer graphene
• Critical Behavior of Four-Terminal Conductance of Bilayer Graphene Domain Walls
• Localized surfaces of three dimensional topological insulators
• Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems
• Scattering of topological kink-antikink states in bilayer graphene structures
• Epitaxially defined Luttinger liquids on MoS${}_2$ bicrystals
• Theory of valley-dependent transport in graphene-based lateral quantum structures
• Quantum Hall interferometry in triangular domains of marginally twisted bilayer graphene
• Signature of multilayer graphene strain-controlled domain walls in quantum Hall effect
• Topologically protected gap states and resonances in gated trilayer graphene
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Localized states coupled to a network of chiral modes in minimally twisted bilayer graphene
• Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers
• Non-chiral one-dimensional states propagating inside AB/BA domain walls in bilayer graphene
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene
• Single layer graphene with electronic properties as gated bilayer
• Physical Origin of Current Partition at a Topological Trifurcation
• Valley selecting current partition at zero-line mode of quantum anomalous Hall topologies
• Movable Dirac Points with Ferroelectrics: Kink States and Berry Curvature Dipoles
• Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer-graphene Corbino disks
• Structural and electronic signatures of strain-tunable marginally twisted bilayer graphene
• Gradient polaritonic surface with space-variant switchable light-matter interactions in 2D moire superlattices
• A Quantized Interband Topological Index in Two-Dimensional Systems
• Effects of domain walls in bilayer graphene in an external magnetic field
• Zigzag nanoribbon of gated bilayer hexagonal crystals with spontaneous edge magnetism
• Photonic emulation of two-dimensional materials with antiferromagnetic order
• Tutorial: Topology, waves, and the refractive index
• Conductance of electrostatic wire junctions in bilayer graphene
• Josephson junction of minimally twisted bilayer graphene
• Strain-tunable synthetic gauge fields in topological photonic graphene
• Chiral states around a mass-inverted quantum dot in graphene
• Hardcore bosonic domain walls on honeycomb lattice
• Topological phase transition of the centered rectangular photonic lattice
• Theory of field-modulated spin-valley-orbital pseudospin physics
• Spin and valley polarized one-way Klein tunneling in photonic topological insulators
• Magnetoconductance of the Corbino disk in graphene: Chiral tunneling and quantum interference in the bilayer case
• Energy symmetry and interlayer wave function ratio of tunneling electrons in partially overlapped graphene
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• The emergence of interface states in graphene/transition metal dichalcogenides heterostructure with lateral interface
• Symmetry breaking, strain solitons and mechanical edge modes in monolayer antimony
• Twisted Type-II Rashba Homobilayer: A Platform for Tunable Topological Flat Bands
• Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides
• Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice
• Nonmonotonic plasmon dispersion in strongly interacting Coulomb Luttinger liquids
• Winding Berry dipole on uniaxially strained graphene/hBN/hBN moiré trilayers
• Large positive magnetoconductance in carbon nanoscrolls
• Topologically protected one-dimensional electronic states in group IV two-dimensional Dirac materials
• Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene
• Direct observation of magneto-electric Aharonov-Bohm effect in moiré-scale quantum paths of minimally twisted bilayer graphene
• Local Optical Conductivity of Bilayer Graphene with Kink Potential
• Spatial variation of energy gap and Landau levels around gapped bilayer graphene domain walls
• Controlling the Interferometers of Zero-Line Modes in Graphene by Pseudomagnetic field
• Tunable lattice reconstruction and bandwidth of flat bands in magic-angle twisted bilayer graphene
• Topological invariant of multilayer Haldane models with irregular stackings
• Network model and four-terminal transport in minimally twisted bilayer graphene
• Effects of spin-orbit coupling in a valley chiral kagomé network
• A general relation between stacking order and Chern index: a topological map of minimally twisted bilayer graphene
• Proximity spin-orbit coupling in graphene on alloyed transition metal dichalcogenides
• Connection between the semiconductor--superconductor transition and the spin-polarized superconducting phase in the honeycomb lattice
• Local optical conductivity of strain solitons in bilayer graphene with arbitrary soliton angle
• Semiconductor Meta-Graphene and Valleytronics
• Twisted bilayer graphene as a terahertz plasmonic crystal
• Electrostatic tuning of bilayer graphene edge modes