Speaker
Bogdan Bernevig
Description
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. 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, the fermionic spin-1 generalization of a Weyl
fermion, and the existence of Dirac lines. In addition, we
present 18 candidate materials that should realize these
exotic fermions, as verified by ab-initio calculations. We also
present holographic fermions - fermions that can appear only
at the boundary of higher dimensional insulators, and show
that their connectivity in the Brillouin zone is described by an
extension of Group Cohomology to the Brillouin zone. For all
these systems we present realistic materials.
