{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T06:03:54Z","timestamp":1784613834336,"version":"3.55.0"},"reference-count":52,"publisher":"IOP Publishing","issue":"29","license":[{"start":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T00:00:00Z","timestamp":1784592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T00:00:00Z","timestamp":1784592000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys.: Condens. Matter"],"published-print":{"date-parts":[[2026,7,24]]},"abstract":"Abstract<\/jats:title>\n \n We derive a low-energy\n \n \n \n <\/jats:tex-math>\n \n \n \n k<\/mml:mi>\n <\/mml:mrow>\n \u22c5<\/mml:mo>\n \n p<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n effective Hamiltonian for monolayer osmium carbide (OsC) and ruthenium carbide (RuC) in a planar hexagonal configuration. First-principles calculations indicate that both monolayers are dynamically stable and exhibit features of a two-dimensional quantum spin Hall phase, characterized by a nontrivial\n \n \n \n <\/jats:tex-math>\n \n \n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n topological invariant. Using symmetry analysis at the\n \n \n \n <\/jats:tex-math>\n \n \n \u0393<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n point, we construct a multiband\n \n \n \n <\/jats:tex-math>\n \n \n \n k<\/mml:mi>\n <\/mml:mrow>\n \u22c5<\/mml:mo>\n \n p<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n Hamiltonian including spin\u2013orbit coupling and reduce it to a four-band low-energy model through L\u00f6wdin partitioning. The effective Hamiltonian has a block-diagonal form, with two blocks related by time-reversal symmetry, analogous to the Bernevig\u2013Hughes\u2013Zhang (BHZ) model. In contrast to the standard BHZ form, the symmetry-allowed off-diagonal coupling contains quadratic momentum-dependent terms, which modify the low-energy dispersion near the\n \n \n \n <\/jats:tex-math>\n \n \n \u0393<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n point. The fitted parameters reproduce the\n ab initio<\/jats:italic>\n band structures in the low-energy region, yielding a compact model for analyzing the electronic and topological properties of monolayer OsC and RuC.\n <\/jats:p>","DOI":"10.1088\/1361-648x\/ae88a5","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T22:53:56Z","timestamp":1783637636000},"page":"295301","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry-constrained low-energy effective Hamiltonian for topological RuC and OsC monolayers"],"prefix":"10.1088","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9856-5573","authenticated-orcid":true,"given":"A","family":"Baradaran","sequence":"first","affiliation":[{"name":"University of Qom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2188-3776","authenticated-orcid":false,"given":"O","family":"Sedaghatfar","sequence":"additional","affiliation":[{"name":"Islamic Azad University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,7,21]]},"reference":[{"key":"cmae88a5bib1","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1126\/science.1174736","type":"journal-article","article-title":"Nonlocal transport in the quantum spin Hall state","volume":"325","author":"Roth","year":"2009","journal-title":"Sci."},{"key":"cmae88a5bib2","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1021\/acs.jpclett.7b00222","type":"journal-article","article-title":"Two-dimensional topological insulators: progress and prospects","volume":"8","author":"Kou","year":"2017","journal-title":"J. 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