Differential topology of semimetals

Abstract

The subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields. Part of this story is the relationship between cohomological semimetal invariants, Euler structures, and ambiguities in the torsion of manifolds. Dually, a topological semimetal can be represented by Euler chains from which its surface Fermi arc connectivity can be deduced. These dual pictures, and the link to topological invariants of insulators, are organised using geometric exact sequences. We go beyond Dirac-type Hamiltonians and introduce new classes of semimetals whose local charges are subtle Atiyah-Dupont-Thomas invariants globally constrained by the Kervaire semicharacteristic, leading to the prediction of torsion Fermi arcs.

44pp, CMP (to appear)

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Cited by in corpus (28)

• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Revealing tensor monopoles through quantum-metric measurements
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Soft self-assembly of Weyl materials for light and sound
• Fermi arc reconstruction at junctions between Weyl semimetals
• Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Invariants of disordered semimetals via the spectral localizer
• Non-Abelian tensor Berry connections in multi-band topological systems
• Tensor Monopoles in superconducting systems
• T-duality simplifies bulk-boundary correspondence: the noncommutative case
• Fu-Kane-Mele monopoles in semimetals
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Tensor monopoles and negative magnetoresistance effect in optical lattices
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Doubling Theorem and Boundary States of Five-Dimensional Weyl Semimetal
• T-duality and the bulk-boundary correspondence
• On spectral flow and Fermi arcs
• The Fermi gerbe of Weyl semimetals
• Five-dimensional Floquet topological semimetals with emergent Yang monopoles and linked Weyl surfaces
• Winding Topology of Multifold Exceptional Points
• Fractional quantum numbers via complex orbifolds
• Weyl semimetals and spin${}^c$ cobordism
• Topological Semimetals
• Three-dimensional spinless Euler insulators with rotational symmetry
• The analytically tractable zoo of similarity-induced exceptional structures
• Homological bulk-edge correspondence for Weyl semimetal