Weyl and Dirac semimetals with Z_2 topological charge

Abstract

We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with ${\mathbb{Z}}_2$ topological charge are stable in a semimetal with time-reversal and reflection symmetries when the square of the product of the two symmetry transformations equals minus identity. We present toy models of ${\mathbb{Z}}_2$ Weyl semimetals which have surface modes forming helical Fermi arcs. We also show that Dirac points with ${\mathbb{Z}}_2$ topological charge are stable in a semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries when the square of the product of time-reversal and inversion equals plus identity. Furthermore, we briefly discuss the topological stability of point nodes in superconductors using Clifford algebras.

14 pages, 2 figures

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Topological Fermi arcs in superfluid ${}^3$He
• Majorana edge modes of superfluid 3He A-phase in a slab
• Topology of the planar phase of superfluid ${}^3$He and bulk-boundary correspondence for three dimensional topological superconductors

Cited by in corpus (76)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe${}_2$
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian topological phenomena: A review
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Topological Semimetals from first-principles
• Thermoelectric properties of Weyl and Dirac semimetals
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Topological surface states in nodal superconductors
• Are the double Fermi arcs of Dirac semimetals topologically protected?
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Crossed surface flat bands of Weyl semimetal superconductors
• Magnetic catalysis and axionic charge-density-wave in Weyl semimetals
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Stiefel-Whitney classes and topological phases in band theory
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• Three-dimensional photonic Dirac points stabilized by point group symmetry
• Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
• Topological carbon materials: a new perspective
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Type-II Dirac Photons
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Discovering topological surface states of Dirac points
• Topologically stable gapless phases in nonsymmorphic superconductors
• Theory for spin torque in Weyl semimetal with magnetic texture
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Zero-index Weyl metamaterials
• Heart and diamond Fermi arcs in Pd and Pt oxide topological Dirac semimetals
• Non-Abelian tensor Berry connections in multi-band topological systems
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• A Weyl-${\mathrm{Z}}_2$ semimetal from holography
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Probing helicity and the topological origins of helicity via non-local Hanbury-Brown and Twiss correlations
• Stable Dirac semi-metal in the allotrope of IV elements
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors
• $2\pi$-flux loop semimetals
• Chiral topological insulating phases from three-dimensional nodal loop semimetals
• Spin-orbit crossed susceptibility in topological Dirac semimetals
• Nonlinear Chiral Transport in Dirac Semimetals
• Zeros of Green Functions in Topological Insulators
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Semi-Quantized Spin Pumping and Spin-Orbit Torques in Topological Dirac Semimetals
• Multiplicative topological semimetals
• Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries
• Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors
• Characterization of Lifshitz transitions in topological nodal line semimetals
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Ferromagnetic-electrodes-induced Hall effect in topological Dirac semimetals
• Parallel and anti-parallel helical surface states for topological semimetals
• Topological phase transitions of semimetal states in effective field theory models
• Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials
• Geometric semimetals and their simulation in synthetic matter
• Magneto-optical Conductance of Kane Fermion Gas in Low Frequencies
• Floquet composite Dirac semimetals
• Euler band topology in superfluids and superconductors
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Fermionic Casimir effect in the presence of compact dimension in field theory with Lorentz invariance violation
• Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model
• Essentially degenerate hidden nodal lines in two-dimensional magnetic layer groups
• Chiral Anomaly Induced Transverse Planar Transport Phenomena in Three Dimensional Spin-Orbit Coupled Metals
• 2D Gapless Topological Superfluids Generated by Pairing Phases
• Hinge modes of three-dimensional Euler insulators