Edge-of-edge States

Abstract

We study an exotic state which is localized only at an intersection of edges of a topological material. This "edge-of-edge" state is shown to exist generically. We construct explicitly generic edge-of-edge states in 5-dimensional Weyl semimetals and their dimensional reductions, such as 4-dimensional topological insulators of class A and 3-dimensional chiral topological insulators of class AIII. The existence of the edge-of-edge state is due to a topological charge of the edge states. The notion of the Berry connection is generalized to include the space of all possible boundary conditions, where Chern-Simons forms are shown to be nontrivial.

11 pages, 1 figure, references added

References in corpus (9)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Tuning phase transition between quantum spin Hall and ordinary insulating phases
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• Boundary Conditions and Surface States Spectra in Topological Insulators

Cited by in corpus (51)

• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Second-order topological non-Hermitian skin effects
• Mirror skin effect and its electric circuit simulation
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Higher-order Topological Mott Insulators
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Second-order topological phases protected by chiral symmetry
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Symmetry indicators of band topology
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• High-order topological insulators from high-dimensional Chern insulators
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Entanglement polarization for the topological quadrupole phase
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Square-root topological phase with time-reversal and particle-hole symmetry
• Gauge Field Induced Chiral Zero Mode in Five-dimensional Yang Monopole Metamaterials
• Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
• Higher-order topological insulators in a magnetic field
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Exploring topological phase transition andWeyl physics in five dimensions with electric circuits
• Multiorbital edge and corner states in black phosphorene
• A Dirac fermion model associated with second order topological insulator
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Escape from black holes in materials: Type II Weyl semimetals and generic edge states
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Higher-order topological heat conduction on a lattice for detection of corner states
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Toeplitz operators on concave corners and topologically protected corner states
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Interaction-induced quantum spin Hall insulator in the organic Dirac electron system $\alpha$-(BEDT-TSeF)${}_2$I${}_3$
• Topological Edge and Corner States in Biphenylene Network
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Floquet higher-order topological phases in momentum space
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Classification of topological invariants related to corner states
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• The Fermi gerbe of Weyl semimetals
• Mod-two APS index and domain-wall fermion
• Five-dimensional Floquet topological semimetals with emergent Yang monopoles and linked Weyl surfaces
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Understanding the index theorems with massive fermions
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Boundary Condition Analysis of First and Second Order Topological Insulators