New Fermions

Abstract

In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. In this paper, we show that this is not a complete classification. We find the types of crystal symmetry-protected free fermionic excitations that can occur in condensed matter systems, going beyond the classification of Majorana, Weyl, and Dirac particles. This includes the first natural generalization of the Weyl fermion, described by a \(\mathbf{k}\cdot\mathbf{S}\) Hamiltonian. We exhaustively classify linear and quadratic 3-, 6- and 8- 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. For each new class of fermion, we analyze its topological properties by constructing the low-energy effective Hamiltonian and comment on any possible experimental signatures. Some notable consequences of these fermions are the presence of Fermi arcs in non-Weyl systems, and the existence of Dirac lines. In addition, we present 17 existing materials (and 22 additional materials in the Supplement) that realize these exotic fermion close to the fermi level, as verified by ab-initio calculations. Finally, we comment on experimental investigations that are currently underway.