Hopf Semimetals

Abstract

We construct two-band topological semimetals in four dimensions using the unstable homotopy of maps from the three-torus $T^3$ (Brillouin zone of a 3D crystal) to the two-sphere $S^2$. Dubbed ``Hopf semimetals'', these gapless phases generically host nodal lines, with a surface enclosing such a nodal line in the four-dimensional Brillouin zone carrying a Hopf flux. These semimetals show a unique class of surface states: while some three-dimensional surfaces host gapless Fermi-arc states {\em and} drumhead states, other surfaces have gapless Fermi surfaces. Gapless two-dimensional corner states are also present at the intersection of three-dimensional surfaces.

arXiv comment5 pages, 4 figures + Supplemental Material (4 pages, 2 figures)

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Cited by in corpus (2)

• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Correlated Hopf insulators