Mobile Majorana zero-modes in two-channel Kondo lattices

Non-abelian anyons are highly desired for topological quantum computation purposes, with Majorana fermions a promising possibility, particularly localized zero modes with non-trivial mutual statistics. Yet realizing Majorana zero modes in matter is a challenge, with proposals in fractional quantum hall states, chiral superconductors and spin liquids, but no clear successes. Heavy fermion materials have long been known to host Majoranas at two-channel Kondo impurities, however, these impurities are difficult to manipulate, and moreover occur in metals, where Majoranas at different impurities can communicate and lose their topological nature. Here, we show that topological defects in a lattice of these two-channel Kondo impurities can also host Majoranas, but can be engineered to avoid the above difficulties, providing the novel possibility of non-trivial, stable and manipulable Majorana zero modes in a two-channel Kondo insulator. We examine this effect in a simple square octagon model at quarter filling with an antiferrohastatic order that opens up a hybridization gap at the quadratic band touching point and show that skyrmionic defects in this state host Majorana zero modes.