One-dimensional 2n-root topological insulators and superconductors

Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to 2(n)-root topological insulators and superconductors, with n any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of 2(n)-root topological insulators/superconductors which connects the Hamiltonian of the starting model for any n through a series of squaring operations followed by constant energy shifts to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of 2(n)-root topology to higher-dimensional systems.

Automated summary

Square-root topology is a newly emerged subfield that describes a class of insulators and superconductors whose topological nature is only revealed after squaring their Hamiltonians. The concept can be generalized to 2(n)-root topological insulators and superconductors, with n as any positive integer, with their construction rules systematized. This work opens the way for extending 2(n)-root topology to higher-dimensional systems.