2011/09/30 by Juan L. Mañes, Juan L. Manes · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Brillouin zone #Chiral anomaly #Condensed matter physics #Coupling (piping) #Crystal (programming language) #Dirac (video compression format) #Fermion #Geometry #Graphene research and applications #Materials science #Mathematics #Physics #Quantum mechanics #Space (punctuation) #Spin (aerodynamics) #Symmetry (geometry) #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.85.155118
published as Phys. Rev. B 85, 155118 (2012) · 8 pages, 4 figures. References added, improved presentation
arxiv created 2012/03/29 · openalex publication_date 2012/04/10 · arxiv updated 2012/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic three-dimensional (3D) crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely, that of nonmagnetic 3D crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some of the issues.