Abstract
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 -root topological insulators and superconductors, with any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of -root topological insulators/superconductors which connects the Hamiltonian of the starting model for any 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 -root topology to higher-dimensional systems.
8 More- Received 12 March 2021
- Revised 27 May 2021
- Accepted 9 June 2021
DOI:https://doi.org/10.1103/PhysRevB.103.235425
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