Topological band crossings in hexagonal materials

Abstract

Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states and unusual magneto-transport properties. In this paper, we present a complete classification of all possible nonsymmorphic band degeneracies in hexagonal materials with strong spin-orbit coupling. This includes (i) band crossings protected by conventional nonsymmorphic symmetries, whose partial translation is within the invariant space of the mirror/rotation symmetry; and (ii) band crossings protected by off-centered mirror/rotation symmetries, whose partial translation is orthogonal to the invariant space. Our analysis is based on (i) the algebraic relations obeyed by the symmetry operators and (ii) the compatibility relations between irreducible representations at different high-symmetry points of the Brillouin zone. We identify a number of existing materials where these nonsymmorphic nodal lines are realized. Based on these example materials, we examine the surface states that are associated with the topological band crossings. Implications for experiments and device applications are briefly discussed.

arXiv comment16 pages, 15 figures, 4 tables

References in corpus (45)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Classification of topological quantum matter with symmetries
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Experimental discovery of Weyl semimetal TaAs
• Topological Insulator Materials
• Topological nodal semimetals
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Topological quantum chemistry
• Topological nodal line semimetals with and without spin-orbital coupling
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Dirac Cone Protected by Non-Symmorphic Symmetry and 3D Dirac Line Node in ZrSiS
• Dirac Semimetals in Two Dimensions
• Topological classification of crystalline insulators through band structure combinatorics
• Nodal-chain metals
• Topology of crystalline insulators and superconductors
• A new type of Weyl semimetal with quadratic double Weyl fermions in SrSi2
• Topological semi-metals with line nodes and drumhead surface states
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Weyl Metals
• Stability of Fermi Surfaces and K-Theory
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAgX (X = P, As)
• Twisted equivariant matter
• Existence of bulk chiral fermions and crystal symmetry
• Topological Classification and Stability of Fermi Surfaces
• Symmetry Demanded Topological Nodal-line Materials
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Topological Insulators from Group Cohomology
• Graph Theory Data for Topological Quantum Chemistry
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Topological transport in Dirac nodal-line semimetals
• Spinless hourglass nodal-line semimetals
• Quantum anomalies in nodal line semimetals
• Topological Materials Discovery using Electron Filling Constraints
• Weyl points and Dirac lines protected by multiple screw rotations
• Hourglass semimetals with nonsymmorphic symmetries in three dimensions
• Mirror Anomaly in Dirac Semimetals

Cited by in corpus (34)

• Higher-order Dirac fermions in three dimensions
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• Kramers Nodal Line Metals
• Field-tunable toroidal moment and anomalous Hall effect in noncollinear antiferromagnetic Weyl semimetal Co1/3TaS2
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Exhaustive List of Topological Hourglass Band Crossings in 230 Space Groups
• High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
• Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals
• Anisotropic phonon-mediated electronic transport in chiral Weyl semimetals
• Collinear Rashba-Edelstein effect in non-magnetic chiral materials
• Superconductivity of anomalous pseudospin
• Chiralities of nodal points along high symmetry lines with screw rotation symmetry
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Symmetry-enforced nodal lines in the band structures of vacancy-engineered graphene
• Topological electronic structure and Weyl points in nonsymmorphic hexagonal materials
• Filling-enforced Dirac loops and their evolutions under various perturbations
• Movable but not removable band degeneracies in a symmorphic crystal
• $n$-Hourglass Weyl fermions in nonsymmorphic materials
• Upper bound of a band complex
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Electronic structures near unmovable nodal points and lines in two-dimensional materials
• Electronic Structure of Kramers Nodal-Line Semimetal YAuGe and Anomalous Hall Effect Induced by Magnetic Rare-Earth Substitution
• Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials
• Correlation Induced Magnetic Topological Phases in Mixed-Valence Compound SmB6
• Electronic interactions in a vacancy-engineered honeycomb lattice: Transition from a nodal-line semimetal to a magnetic insulator
• Less is more: Vacancy-engineered nodal-line semimetals
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Phonon Weyl points and chiral edge modes with unconventional Fermi arcs in NbSi${}_2$
• CeAu${}_2$Bi: a new nonsymmorphic antiferromagnetic compound