{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:54:14Z","timestamp":1787028854438,"version":"build-2736575974"},"reference-count":47,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T00:00:00Z","timestamp":1742688000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Research Project of Hebei Education Department","award":["QN2023056"],"award-info":[{"award-number":["QN2023056"]}]},{"name":"Science Research Project of Hebei Education Department","award":["BJK2023013"],"award-info":[{"award-number":["BJK2023013"]}]},{"name":"Science Research Project of Hebei Education Department","award":["20230500100101221"],"award-info":[{"award-number":["20230500100101221"]}]},{"name":"The Sixth \u201c333 Talents\u201d Training Support Project of Jiangsu Province","award":["QN2023056"],"award-info":[{"award-number":["QN2023056"]}]},{"name":"The Sixth \u201c333 Talents\u201d Training Support Project of Jiangsu Province","award":["BJK2023013"],"award-info":[{"award-number":["BJK2023013"]}]},{"name":"The Sixth \u201c333 Talents\u201d Training Support Project of Jiangsu Province","award":["20230500100101221"],"award-info":[{"award-number":["20230500100101221"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Revealing singular quantum phenomena in various non-Hermitian systems is a hot topic in condensed matter physics research, with the bulk-boundary correspondence being one of the core issues in non-Hermitian topological states. In addition, the spin-orbit coupling (SOC) applied to electrons moving in the electric field in the material can bring unique topological properties to the energy band of the material. We investigated the topological phase transition of a non-Hermitian Su\u2013Schrieffer\u2013Heeger (SSH) model with SOC in the generalized Brillouin zone (GBZ). We demonstrate that SOC can alter the position and number of phase transition points. Due to the non-Hermitian skin effect, the bulk-boundary correspondence is broken, and the local positions of zero mode and bulk eigenstates will also change. By unitary transformation, two subspaces were obtained, and the exact solution of topological phase transition was obtained in the GBZ. The exact solution of non-Hermitian systems with the Dresselhaus and Rashba types of SOC is consistent with the numerical solutions. This result can be applied to more complex non-Hermitian models, providing a strong reference for experimental researchers in topological materials.<\/jats:p>","DOI":"10.3390\/ma18071417","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T04:48:18Z","timestamp":1742791698000},"page":"1417","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Topological Phases of One-Dimensional Non-Hermitian Systems with Spin-Orbit Coupling of the Generalized Brillouin Zone"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4437-8749","authenticated-orcid":false,"given":"Yanzhen","family":"Han","sequence":"first","affiliation":[{"name":"College Electronics Information Engineering, Hengshui University, Hengshui 053000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianxiao","family":"Liu","sequence":"additional","affiliation":[{"name":"College Electronics Information Engineering, Hengshui University, Hengshui 053000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5429-6255","authenticated-orcid":false,"given":"Shiyao","family":"Chong","sequence":"additional","affiliation":[{"name":"College Electronics Information Engineering, Hengshui University, Hengshui 053000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingjing","family":"Du","sequence":"additional","affiliation":[{"name":"College Electronics Information Engineering, Hengshui University, Hengshui 053000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linghui","family":"Meng","sequence":"additional","affiliation":[{"name":"College Electronics Information Engineering, Hengshui University, Hengshui 053000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingjie","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Jinling Institute of Technology, Nanjing 211169, China"},{"name":"School of Transportation, Southeast University, Nanjing 210009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1103\/RevModPhys.83.1057","article-title":"Topological insulators and superconductors","volume":"83","author":"Qi","year":"2011","journal-title":"Rev. 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