Inversion-symmetric topological insulators in cut-and-project binary chains
Abstract
We investigate the electronic properties of binary tight-binding chains generated by the cut-and-project method for rational slopes α=p/q, leading to periodic and inversion symmetric chains with n=p+q sites. The binary structure is encoded in two hopping amplitudes ta and tb. For fixed ta ≠ tb, the support of the energy spectrum as a function of p/n gives rise to a "Cut-and-Project butterfly". We concentrate on insulators with M filled bands among a total of n bands and vary ta/tb. Inversion symmetry constrains the electric polarization P to $0$ or Pq/2 modulo a polarization quantum Pq = gcd(M,n)/n. A topological transition, between two insulators that differ by their quantized polarization, occurs if and only if n/gcd(M,n) is odd. When n/gcd(M,n) is even, the two insulating regimes have a vanishing polarization and no topological transition occurs, despite the gap closing at ta=tb. When n is even and M odd, we find an adiabatic path between ta>tb and ta<tb that maintains inversion symmetry and a gap.
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BibTeX
@misc{zeng2026inversionsymmetric,
title = {{Inversion-symmetric topological insulators in cut-and-project binary chains}},
author = {Zhipeng Zeng and Yuge Chen and Jean-Noël Fuchs and Jianxin Zhong and Rémy Mosseri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01312},
eprint = {2609.01312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01312},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inversion-symmetric topological insulators in cut-and-project binary chains
AU - Zhipeng Zeng
AU - Yuge Chen
AU - Jean-Noël Fuchs
AU - Jianxin Zhong
AU - Rémy Mosseri
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01312
UR - https://arxiv.org/abs/2609.01312
AB - We investigate the electronic properties of binary tight-binding chains generated by the cut-and-project method for rational slopes α=p/q, leading to periodic and inversion symmetric chains with n=p+q sites. The binary structure is encoded in two hopping amplitudes t_a and t_b. For fixed t_a ≠ t_b, the support of the energy spectrum as a function of p/n gives rise to a "Cut-and-Project butterfly". We concentrate on insulators with M filled bands among a total of n bands and vary t_a/t_b. Inversion symmetry constrains the electric polarization P to $0$ or P_q/2 modulo a polarization quantum P_q = gcd(M,n)/n. A topological transition, between two insulators that differ by their quantized polarization, occurs if and only if n/gcd(M,n) is odd. When n/gcd(M,n) is even, the two insulating regimes have a vanishing polarization and no topological transition occurs, despite the gap closing at t_a=t_b. When n is even and M odd, we find an adiabatic path between t_a>t_b and t_a<t_b that maintains inversion symmetry and a gap.
ER -