Topological Classification and Stability of Fermi Surfaces

Abstract

In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.

5 pages, published version in PRL

References in corpus (3)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Simplified topological invariants for interacting insulators

Cited by in corpus (137)

• Classification of topological quantum matter with symmetries
• Topology of crystalline insulators and superconductors
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Topological semi-metals with line nodes and drumhead surface states
• Non-Hermitian topological phenomena: A review
• Nodal surface semimetals: Theory and material realization
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Topological quantum matter with cold atoms
• Tunable Weyl Points in Periodically Driven Nodal Line Semimetals
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Multi-terminal Josephson junctions as topological materials
• Type-II nodal loops: theory and material realization
• Nodal-knot semimetals
• Topological surface states in nodal superconductors
• Quantum transport of disordered Weyl semimetals at the nodal point
• Are the double Fermi arcs of Dirac semimetals topologically protected?
• Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe${}_6$ ($X=$ Ta, Nb)
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Hourglass Dirac Chain Metal in Rhenium Dioxide
• Computation and data driven discovery of topological phononic materials
• Coexistence of four-band nodal rings and triply-degenerate nodal points in centrosymmetric metal diborides
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Artificial gravity field, astrophysical analogues, and topological phase transitions in strained topological semimetals
• Nodal Loop and Nodal Surface States in Ti3Al Family Materials
• Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications
• Quadratic and Cubic Nodal Lines Stabilized by Crystalline Symmetry
• Topological and geometrical aspects of band theory
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• 4D spinless topological insulator in a periodic electric circuit
• Topological Blount's theorem of odd-parity superconductors
• Topological transport in Dirac nodal-line semimetals
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Weyl and Dirac semimetals with Z_2 topological charge
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Hybrid Dirac Semimetal in CaAgBi Materials Family
• Quadratic contact point semimetal: Theory and material realization
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• $d$-Orbital Topological Insulator and Semimetal in Antifluorite Cu${}_2$S Family: Contrasting Spin Helicities, Nodal Box, and Hybrid Surface States
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Weyl-loop half metal in Li${}_3$(FeO${}_3$)${}_2$
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• A Family Group of Two-dimensional Node-Line Semimetals
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
• Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
• Floquet multi-Weyl points in crossing-nodal-line semimetals
• Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
• Switching spinless and spinful topological phases with projective $PT$ symmetry
• Weyl nodal surfaces
• Topological surface superconductivity in doped Weyl loop materials
• Topologically stable gapless phases in nonsymmorphic superconductors
• The gauge-field extended $k\cdot p$ method and novel topological phases
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• Magnetic higher-order nodal lines
• Conversion rules for Weyl points and nodal lines in topological media
• Superconductivity in doped inversion-symmetric Weyl semimetals
• Topological spinon semimetals and gapless boundary states in three dimensions
• Topological band crossings in hexagonal materials
• Differential topology of semimetals
• Edge currents as a signature of flat bands in topological superconductors
• Fragile surface zero-energy flat bands in three-dimensional chiral superconductors
• Crystalline Kitaev spin liquids
• Almost ideal nodal-loop semimetal in monoclinic CuTeO${}_3$ material
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Weyl Semimetal and Topological Phase Transition in Five Dimensions
• Deformation and Stability of Surface States in Dirac semimetals
• Chern-Simons Theory and Wilson Loops in the Brillouin Zone
• Global topology of Weyl semimetals and Fermi arcs
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Circular Dichroism and Radial Hall Effects in Topological Materials
• Disordered Weyl semimetals and their topological family
• Realizing and manipulating space-time inversion symmetric topological semimetal bands with superconducting quantum circuits
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Index theorem on chiral Landau bands for topological fermions
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Interface currents in topological superconductor-ferromagnet heterostructures
• Dimensional crossover of effective orbital dynamics in polar distorted 3He-A: Transitions to anti-spacetime
• Surface transport coefficients for three-dimensional topological superconductors
• Exotic Topological Types of Majorana Zero-modes and Their Universal Quantum Manipulation
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• Further insights into the thermodynamics of the Kitaev honeycomb model
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Topological Gapless Phases in Non-Symmorphic Antiferromagnets
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Composite Dirac Semimetal
• PT invariant Weyl semimetals in gauge symmetric systems
• Symmetry-protected non-Fermi liquids, Kagome spin liquids, and the chiral Kondo lattice model
• Magneto-transport and Shubnikov-de Haas oscillations in the layered ternary telluride Ta3SiTe6 topological semimetal
• Topological $s$-wave superconductors driven by electron correlation
• Topological Classification of Excitations in Quadratic Bosonic Systems
• Large Chern Number Topological Superfluids in Coupled Layer System
• Surface instability in nodal noncentrosymmetric superconductors
• Topological nature of step edge states on the surface of topological crystalline insulator Pb${}_{0.7}$Sn${}_{0.3}$Se
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• Definition and Classification of Fermi Surface Anomalies
• Drumhead surface states and their signatures in quasiparticle scattering interference
• Doubling Theorem and Boundary States of Five-Dimensional Weyl Semimetal
• Chiral spin liquids with crystalline ${\mathbb{Z}}_2$ gauge order in a three-dimensional Kitaev model
• Nodal Line Entanglement Entropy: Generalized Widom Formula from Entanglement Hamiltonians
• Spin, orbital and topological order in models of strongly correlated electrons
• Revealing Majorana Fermion states in a superfluid of cold atoms subject to a harmonic potential
• Periodic Clifford symmetry algebras on flux lattices
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Revealing the spatial nature of sublattice symmetry
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Multi higher-order Dirac and nodal line semimetals
• Topological Insulators with Hybrid-order Boundary States
• Emulating topological currents arising from a dipolar parity anomaly in two-dimensional optical lattices
• Observation of a flat and extended surface state in a topological semimetal
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices
• Takagi topological insulator with odd $\mathcal{P}\mathcal{T}$ pairs of corner states
• Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices
• Local and global patterns in quasiparticle interference: a reduced response function approach
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Topological semimetals and insulators in three-dimensional honeycomb materials
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
• Realizing universal quantum gates with topological bases in quantum-simulated superconducting chains
• Takagi Topological Insulator on the Honeycomb Lattice
• General response theory of topologically stable Fermi points and its implications for disordered cases
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Nodal-line semimetals and their variance
• Emergent topology in thin films of nodal line semimetals
• Spinless topological chirality from Umklapp scattering in twisted 3D structures
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Emergence of Type-I and Type-II Dirac line nodes in penta-octa-graphene
• Theory of Hofstadter Superconductors
• Josephson junctions of topological nodal superconductors
• Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model