Massless multifold Hopf semimetals

Abstract

Three-dimensional topological semimetals exhibit linear energy band crossing points that act as monopoles of Berry curvature. Here, an alternative class of semimetals is introduced, featuring linear $N$-fold crossing points each of which acts as a source of a \emph{Berry dipole}. We construct continuum and lattice models for such \emph{massless multifold Hopf semimetals (MMHSs)} with $N=3,4,5$ bands and study nontrivial effects of a Berry dipole crossing: (i) A Landau level spectrum that is strongly tunable by the orientation of the magnetic field relative to the dipole axis. (ii) An anomalous Hall conductivity that is an odd function of the Fermi level. (iii) Weak-field dissipative magnetoconductivities that resemble the chiral anomaly, chiral magnetic and magnetochiral effects familiar from a pair of coupled Weyl nodes, but that are even functions of the Fermi level. By gapping out MMHSs, multiband Hopf insulators with Hopf numbers as high as ${\mathcal{N}}_{\text{Hopf}}=10$ are obtained, providing a fertile playground to explore delicate topology.

Published version

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Cited by in corpus (8)

• Dipolar Weyl semimetals
• Berry-dipole Semimetals
• Geometric semimetals and their simulation in synthetic matter
• PT-symmetric Non-Hermitian Hopf Metal
• Hopf Semimetals
• Scattering of a Dirac particle by a Berry phase domain wall
• Correlated Hopf insulators
• Quantum geometric scattering of a Dirac particle by a Berry curvature domain wall