Invariants of disordered semimetals via the spectral localizer

Abstract

The spectral localizer consists of placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this technique is extended to disordered semimetals and allows to access the number of Dirac or Weyl points as well as weak invariants. These latter invariants imply the existence of surface states.

arXiv commentto appear in Europhys. Lett

References in corpus (19)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Weyl Semimetal in a Topological Insulator Multilayer
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Spatially Resolving Spin-split Edge States of Chiral Graphene Nanoribbons
• Quantized circular photogalvanic effect in Weyl semimetals
• The Zak phase and the existence of edge states in graphene
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Chern-Simons Currents and Chiral Fermions on the Lattice
• Aperiodic Weak Topological Superconductors
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Theory of the strongly disordered Weyl semimetal
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Differential topology of semimetals
• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Vanishing density of states in weakly disordered Weyl semimetals
• Gap closing and universal phase diagrams in topological insulators
• Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants

Cited by in corpus (16)

• Local invariants identify topology in metals and gapless systems
• An operator-based approach to topological photonics
• Local markers for crystalline topology
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
• Spectral localizer for line-gapped non-hermitian systems
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels
• Topological diffusive metal in amorphous transition metal monosilicides
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Real-space topological invariant for time-quasiperiodic Majoranas
• Even spheres as joint spectra of matrix models
• Local and energy-resolved topological invariants for Floquet systems
• Topological zero-modes of the spectral localizer of trivial metals
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Dimensional crossover of class D real-space topological invariants