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arXiv · 2508.12066

High-root topological edge-state bands

R. G. Dias·L. Madail·A. M. Marques
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Abstract

This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A simplified topological characterization of HRTIs with generalized boundary conditions is carried out based on the existence of edge-state bands in the infinite HRTI and the restrictions imposed by the boundary conditions. Edge states in finite or semi-infinite 1D HRTIs are shown to be a subset of evanescent states of the infinite system and mapped onto impurity states of the uniform chain with effective energy-dependent edge potentials. The latter result allows the determination of the edge state levels without needing the diagonalization of real space or bulk Hamiltonians.

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R. G. Dias, L. Madail, A. M. Marques. 2025-08-16. High-root topological edge-state bands. https://doi.org/10.1103/nf7r-9wb6

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