Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals - Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun; Vergniory, M. G.; Felser, C.; Cava, R. J.; Bernevig, B. Andrei (Science (American Association for the Advancement of Science), 2016)
In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here, we show that in solid-state systems this classification is incomplete, and we find several additional types of crystal symmetry–protected free fermionic excitations. We exhaustively classify linear and quadratic three-, six-, and eight-band crossings stabilized by space group symmetries in solid-state systems with spin-orbit coupling and time-reversal symmetry. Several distinct types of fermions arise, differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. Some notable consequences of these fermions are the presence of Fermi arcs in non-Weyl systems and the existence of Dirac lines. Ab initio calculations identify a number of materials that realize these exotic fermions close to the Fermi level.