Unconventional Topological Insulators from Extended Topological Band Degeneracies
arXiv:2005.03674 · doi:10.1103/PhysRevB.102.115151
Abstract
A general and beautiful picture for the realization of topological insulators is that the mass term of the Dirac model has a nodal surface wrapping one Dirac point. We show that this geometric picture based on Dirac points can be generalized to extended band degeneracies with nontrivial topological charges. As the nontrivial topological charges force the extended band degeneracies to be created or annihilated in pairs, when the nodal surface of mass wraps one such extended band degeneracy, the resulting gapped phase must be topologically nontrivial since it cannot adiabatically be deformed into a topologically trivial atomic insulator without closing the energy gap. We use nodal lines carrying a nontrivial monopole charge in three dimensions to illustrate the physics. Notably, because the wrapping surfaces for an extended band degeneracy are diverse, we find that this generalization can bring topological insulators with unconventional pattern of boundary states.
arXiv comment5 pages, 4 figures
References in corpus (53)
- Topological Insulators
- Topological insulators and superconductors
- Topological Insulators with Inversion Symmetry
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Quantized Electric Multipole Insulators
- Topological nodal semimetals
- Higher-Order Topological Insulators
- Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
- -dimensional edge states of rotation symmetry protected topological states
- Reflection symmetric second-order topological insulators and superconductors
- Topological nodal line semimetals with and without spin-orbital coupling
- Higher-Order Topology in Bismuth
- Dirac Line Nodes in Inversion Symmetric Crystals
- Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite CuPdN
- Dirac Cone Protected by Non-Symmorphic Symmetry and 3D Dirac Line Node in ZrSiS
- Topological nodal line semimetals
- Synthetic gauge fields in synthetic dimensions
- Nodal-chain metals
- Topological semi-metals with line nodes and drumhead surface states
- Topological quantum matter in synthetic dimensions
- Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
- Realization of a three-dimensional photonic topological insulator
- Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe (X=Mo,W)
- Three-dimensional topological photonic crystal with a single surface Dirac cone
- Three-Dimensional All-Dielectric Photonic Topological Insulator
- Line of Dirac Nodes in Hyper-Honeycomb Lattices
- Nodal-link semimetals
- Surface State Magnetization and Chiral Edge States on Topological Insulators
- Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
- Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure
- Four-Dimensional Quantum Hall Effect with Ultracold Atoms
- Non-Abelian band topology in noninteracting metals
- Topological Hopf and chain link semimetal states and their application to Co2MnGa (Theory and Materials Prediction)
- Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
- Topological semimetals with double-helix nodal link
- Nodal-knot semimetals
- Topological surface states in three-dimensional magnetic insulators
- Symmetry Demanded Topological Nodal-line Materials
- Experimental discovery of nodal chains
- From Nodal Chain Semimetal To Weyl Semimetal in HfC
- Topological Semimetals in Square-Net Materials
- Topological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon's-Knot, Trefoil-Knot and Other Semimetals
- Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
- Jones polynomial and knot transitions in topological semimetals
- Diagnosis for topological semimetals in the absence of spin-orbital coupling
- Observation of non-Abelian nodal links in photonics
- Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops
- Experimental Observation of Dirac Nodal Links in Centrosymmetric Semimetal TiB
- Observation of a nodal chain with Dirac surface states in TiB2
- Experimental observation of bulk nodal lines and electronic surface states in ZrB
- Symmorphic intersecting nodal rings in semiconducting layers
- Teleportation of Berry curvature on the surface of a Hopf insulator
- Engineering topological phases with a three-dimensional nodal-loop semimetal