Zero-energy Majorana edge modes in the three-dimensional Kitaev model

Abstract

We obtain analytical solutions for zero-energy Majorana edge modes in the three-dimensional Kitaev model on the hyperhoneycomb lattice. We consider three types of edges (zigzag, bearded, and armchair) and find the regions in parameter space where each type of edge mode exists. In the gapless phase, we obtain edge-state solutions which are the drumhead surface states associated with nodal-line semimetals. We also find a correspondence between noninteracting complex fermions and Majorana fermions on bipartite lattices, which explains the equivalence of energy spectrum and eigenmodes of Kitaev model and a corresponding tight-binding model for complex fermions on the same lattice.