  Non-abelian anyons are highly desired for topological quantum computation
purposes, with Majorana fermions providing a promising route, particularly zero
modes with non-trivial mutual statistics. Yet realizing Majorana zero modes in
matter is a challenge, with various proposals in chiral superconductors,
nanowires, and spin liquids, but no clear experimental examples. Heavy fermion
materials have long been known to host Majorana fermions at two-channel Kondo
impurity sites, however, these impurities cannot be moved adiabatically and
generically occur in metals, where the absence of a gap removes the topological
protection. Here, we consider an ordered lattice of these two-channel Kondo
impurities, which at quarter-filling form a Kondo insulator. We show that
topological defects in this state will host Majorana zero modes, or possibly
more complicated parafermions. These states are protected by the insulating gap
and may be adiabatically braided, providing the novel possibility of realizing
topological quantum computation in heavy fermion materials.
