Systematic construction of square-root topological insulators and superconductors
Motohiko Ezawa
Abstract
We propose a general scheme to construct a Hamiltonian H root describing a square root of an original Hamiltonian H original based on the graph theory. The square-root Hamiltonian is defined on the subdivided graph of the original graph of H original , where the subdivided graph is obtained by putting one vertex on each link in the original graph. When H original describes a topological system, there emerge in-gap edge states at nonzero energy in the spectrum of H root , which are the inherence of the topological edge states at zero energy in H original . In this case, H root describes a square-root topological insulator or superconductor. Typical examples are square roots of the Su-Schrieffer-Heeger (SSH) model, the Kitaev topological superconductor model, and the Haldane model. Our scheme is also applicable to non-Hermitian topological systems, where we study an example of a nonreciprocal non-Hermitian SSH model.