2011/11/30 by Chen Fang, Matthew J. Gilbert, Xi Dai +1 · 11 citations
Materials Science · Mathematics · Physics and Astronomy · #2D Materials and Applications #Band gap #Combinatorics #Condensed matter physics #Fermi Gamma-ray Space Telescope #Fermi level #Ferromagnetism #Geometry #Graphene research and applications #Mathematics #Physics #Quantum mechanics #Rotational symmetry #Semimetal #Symmetry (geometry) #Symmetry group #Topological Materials and Phenomena #Topology (electrical circuits) #Weyl semimetal #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.108.266802
published as PRL 108, 266802 (2012) · 4+ pages, 2 figures, 1 table
openalex publication_date 2012/06/27 · arxiv created 2012/11/14 · arxiv updated 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We perform a complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C(6)-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr(2)Se(4) and confirm it is a double-Weyl metal protected by C(4) symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001] axis to the [111] axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group S(6) of that phase. Finally, we discuss experimentally relevant effects including the splitting of multi-Weyl nodes by applying a C(n) breaking strain and the surface Fermi arcs in these new semimetals.