One-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:math>-root topological insulators and superconductors

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 ${2}^{n}$-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.

Topics & Concepts