Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals

• Published in: Science (American Association for the Advancement of Science) Vol. 353; no. 6299; p. 558
• Main Authors: Bradlyn, Barry, Cano, Jennifer, Wang, Zhijun, Vergniory, M. G., Felser, C., Cava, R. J., Bernevig, B. Andrei
• Format: Journal Article
• Language: English
• Published: United States American Association for the Advancement of Science 05.08.2016; The American Association for the Advancement of Science
• Subjects: Classification; Condensed matter physics; Crystals; Exhaust systems; Exhibits; Fermi surfaces; Fermions; Magnetic fields; Mathematical analysis; Quantum theory; RESEARCH ARTICLE SUMMARY; Symmetry
• ISSN: 0036-8075; 1095-9203
• DOI: 10.1126/science.aaf5037

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.