Mobile Majorana zero-modes in two-channel Kondo insulators

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.