Kitaev chain with a fractional twist

The topological nontriviality of insulating phases of matter are by now well understood through topological K theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudometallic component to the topological phase diagram within which the winding number is valued in Q. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a nonintegral winding number. We remark that this is in correspondence with recent paper demonstrating that projective Dirac operators defined in the absence of spinC structure have rational indices.