Majorana flat bands at structured surfaces of nodal noncentrosymmetric superconductors

Abstract

Surfaces of nodal noncentrosymmetric superconductors can host flat bands of Majorana modes, which provide a promising platform for quantum computation if one can find methods for manipulating localized Majorana wave packets. We study the fate of such flat bands when part of the surface is subjected to an exchange field induced by a ferromagnetic insulator. We use exact diagonalization to find the eigenstates and eigenenergies of the Bogoliubov-de Gennes Hamiltonian of a model system, for which an exchange field is applied along a strip on the surface of a slab. We consider different orientations of the strip and the applied field. If the spin polarization of the field-free system along the field direction is sufficiently large perturbation theory predicts that energies of states which are mostly localized on the exchange-field strip are shifted away from zero energy by an amount proportional to the field strength. On the other hand, energies corresponding to states localized on the field-free strip are only weakly affected by the field. Exact diagonalization confirms this. Moreover, we discuss a setup with a small exchange field applied to the previously field-free strip with the goal of introducing a linear dispersion. By switching this dispersion on and off, a wave packet could be moved in a certain direction. We find that in our model system, a linear dispersion can indeed be achieved. The qualitative features of this dispersion can be predicted from the momentum-dependent spin polarization of the field-free surface.