Topological band crossings in hexagonal materials

J. Zhang, Y. H. Chan, C. K. Chiu, M. G. Vergniory, L. M. Schoop, A. P. Schnyder

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states and unusual magnetotransport properties. In this paper, we present a complete classification of all possible nonsymmorphic band degeneracies in hexagonal materials with strong spin-orbit coupling. This includes (i) band crossings protected by conventional nonsymmorphic symmetries, whose partial translation is within the invariant space of the mirror/rotation symmetry; and (ii) band crossings protected by off-centered mirror/rotation symmetries, whose partial translation is orthogonal to the invariant space. Our analysis is based on (i) the algebraic relations obeyed by the symmetry operators and (ii) the compatibility relations between irreducible representations at different high-symmetry points of the Brillouin zone. We identify a number of existing materials where these nonsymmorphic nodal lines are realized. Based on these example materials, we examine the surface states that are associated with the topological band crossings. Implications for experiments and device applications are briefly discussed.

Original languageEnglish (US)
Article number074201
JournalPhysical Review Materials
Issue number7
StatePublished - Jul 11 2018

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Topological band crossings in hexagonal materials'. Together they form a unique fingerprint.

Cite this