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Abstract

It is complicated to promote a continuum quantum theory with fermions to a lattice. This problem is caused by an unexpected appearance of extra states in the lattice theory - the fermion doubling problem. Nielsen and Ninomiya proved in 1981 that under certain conditions, it is actually impossible to find a lattice that simulates a single Weyl fermion. We realize that one of the crucial assumptions in their proof is the conservation of electric charge - a condition which is not held in topological superconductors. A common toy model for topological superconductors is the one-dimensional Kitaev wire. Thus, we propose a similar two-band three-dimensional lattice that has a single Weyl fermion in the low-energy. We find this effective theory by combining the degrees of freedom around the nodal points and then integrating out the extra degrees of freedom using the Schrieffer-Wolff transformation.