Description
Through a systematic symmetry and topology analysis we
establish that three-dimensional chiral superconductors with
strong spin-orbit coupling and odd-parity pairing generically
host low-energy nodal quasiparticles that are spin-non-
degenerate and realize Majorana fermions in three
dimensions. By examining all types of chiral Cooper pairs with
total angular momentum J formed by Bloch electrons with
angular momentum j in crystals, we obtain a comprehensive
classification of gapless Majorana quasiparticles in terms of
energy-momentum relation and location on the Fermi
surface. We show that the existence of bulk Majorana
fermions in the vicinity of spin-selective point nodes is rooted
in the non-unitary nature of chiral pairing in spin-orbit-
coupled superconductors. We address experimental
signatures of Majorana fermions, and find that the nuclear
magnetic resonance spin relaxation rate is significantly
suppressed for nuclear spins polarized along the nodal
direction as a consequence of the spin-selective Majorana
nature of nodal quasiparticles. Furthermore, Majorana nodes
in the bulk have nontrivial topology and imply the presence of
Majorana bound states on the surface that form arcs in
momentum space. We conclude by proposing the heavy
fermion superconductor PrOs4Sb12 and related materials as
promising candidates for non-unitary chiral superconductors
hosting three-dimensional Majorana fermions.
