One-dimensional $2^n$-root topological insulators and superconductors
| Autor: | Marques, A. M., Madail, L., Dias, R. G. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 103, 235425 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.103.235425 |
| Popis: | 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. Comment: 19 pages, 15 figures |
| Databáze: | arXiv |
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