https://doi.org/10.1140/epjb/s10051-026-01153-y
Research - Condensed Matter
Exploring and controlling topological phases in the square-hexagon lattice via Rashba spin-orbit coupling and next-nearest-neighbor hopping
School of Science, Henan Institute of Technology, 453003, Xinxiang, Henan, China
a
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Received:
13
December
2025
Accepted:
11
March
2026
Published online:
5
May
2026
Abstract
Based on the tight-binding model, we systematically investigate the influence of the Rashba spin-orbit coupling and the next-nearest-neighbor (NNN) hopping on the topological properties of the square-hexagon lattice. The 
topological invariant is evaluated numerically via the Fukui–Hatsugai approach. By tracing the evolution of the band gap as functions of the NNN hopping and Rashba spin-orbit coupling (
and 
), we construct comprehensive phase diagrams. Our findings demonstrate that the interplay between the NNN hopping and Rashba spin-orbit coupling can induce topological phase transitions, including transitions between topological insulator (TI) and normal insulator, as well as between TI and metallic state. In the or 
phase diagram, topological phases can be achieved almost for all the filling fractions. To further clarify the topological properties of the system, we compute the edge state spectra and provide a detailed analysis of their distinguishing characteristics in both topological trivial and nontrivial phases. Our work demonstrates the rich topological phase behavior in the square-hexagon lattice under the NNN hopping and Rashba spin-orbit coupling, offering theoretical insights for the design and control of topological states in low-dimensional quantum materials.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
