Systematic construction of square-root topological insulators and superconductors
Motohiko Ezawa
DOI 10.1103/PhysRevResearch.2.033397 · Physical Review Research
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Abstract
We propose a general scheme to construct a Hamiltonian Hroot describing a square root of an original Hamiltonian Horiginal based on the graph theory. The square-root Hamiltonian is defined on the subdivided graph of the original graph of Horiginal, where the subdivided graph is obtained by putting one vertex on each link in the original graph. When Horiginal describes a topological system, there emerge in-gap edge states at nonzero energy in the spectrum of Hroot, which are the inherence of the topological edge states at zero energy in Horiginal. In this case, Hroot 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.
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