Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams

Abstract

We derive two fundamental laws of chiral band crossings: (i) a local constraint relating the Chern number to phase jumps of rotation eigenvalues; and (ii) a global constraint determining the number of chiral crossings on rotation axes. Together with the fermion doubling theorem, these laws describe all conditions that a network of chiral band crossing must satisfy. We apply the fundamental laws to prove the existence of enforced double Weyl points, nodal planes, and generic Weyl points, among others. In addition, we show that chiral space-group symmetries cannot stabilize nodal lines with finite Chern numbers. Combining the local constraint with explicit low-energy models, we determine the generic topological phase diagrams of all multi-fold crossings. Remarkably, we find a four-fold crossing with Chern number 5, which exceeds the previously conceived maximum Chern number of 4. We identify BaAsPt as a suitable material with this four-fold crossing exhibiting Chern number 5 near the Fermi energy.

34 pages, 16 figures

References in corpus (25)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Topological Semimetals
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Progress and prospects in magnetic topological materials
• Multiple types of topological fermions in transition metal silicides
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Chiral anomaly and transport in Weyl metals
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Twofold quadruple Weyl nodes in chiral cubic crystals
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• Exhaustive constructions of effective models in 1651 magnetic space groups
• Complete classification of band nodal structures
• Charge-4 Weyl point: Minimum lattice model and chirality-dependent properties
• Discovery of a maximally charged Weyl point
• Pseudospin 3/2 Fermions, Type-II Weyl Semimetals and Critical Weyl Semimetals in Tricolor Cubic Lattice
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Network of topological nodal planes, multifold degeneracies, and Weyl points in CoSi
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Weyl-like points from band inversions of spin-polarised surface states in NbGeSb
• Spin-momentum locking from topological quantum chemistry: applications to multifold fermions
• Chiralities of nodal points along high symmetry lines with screw rotation symmetry
• A $k\cdot p$ effective Hamiltonian generator
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

Cited by in corpus (10)

• Gapped nodal planes drive a large topological Nernst effect in a chiral lattice antiferromagnet
• Altermagnetic Instabilities from Quantum Geometry
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Geometric semimetals and their simulation in synthetic matter
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Weak ${\mathbb{Z}}_2$ Supertopology
• Quantum geometry and low-frequency optical conductivity of nodal planes
• Fermi surface and topology of multiband superconductor BeAu