{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:38:22Z","timestamp":1791531502190,"version":"4.3.4"},"reference-count":59,"publisher":"IOP Publishing","issue":"19","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/page\/copyright"},{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Core Research for Evolutional Science and Technology (CREST), JST","award":["JPMJCR18T4"],"award-info":[{"award-number":["JPMJCR18T4"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nanotechnology"],"published-print":{"date-parts":[[2024,5,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We unveil that the holey graphyne (HGY), a two-dimensional carbon allotrope where benzene rings are connected by two \u2212C\u2261C\u2212 bonds fabricated recently in a bottom-up way, exhibits topological electronic states. Using first-principles calculations and Wannier tight-binding modeling, we discover a higher-order topological invariant associated with <jats:italic>C<\/jats:italic>\n                  <jats:sub>2<\/jats:sub> symmetry of the material, and show that the resultant corner modes appear in nanoflakes matching to the structure of precursor reported previously, which are ready for direct experimental observations. In addition, we find that a band inversion between emergent <jats:italic>g<\/jats:italic>-like and <jats:italic>h<\/jats:italic>-like orbitals gives rise to a nontrivial topology characterized by <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                     <\/mml:math>\n                  \n                  <\/jats:inline-formula> invariant protected by an energy gap as large as 0.52 eV, manifesting helical edge states mimicking those in the prominent quantum spin Hall effect, which can be accessed experimentally after hydrogenation in HGY. We hope these findings trigger interests towards exploring the topological electronic states in HGY and related future electronics applications.<\/jats:p>","DOI":"10.1088\/1361-6528\/ad2483","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T22:23:57Z","timestamp":1706739837000},"page":"195201","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Topological electronic states in holey graphyne"],"prefix":"10.1088","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9824-0907","authenticated-orcid":false,"given":"Yong-Cheng","family":"Jiang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3746-6803","authenticated-orcid":false,"given":"Toshikaze","family":"Kariyado","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6880-402X","authenticated-orcid":false,"given":"Xiao","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"key":"nanoad2483bib1","doi-asserted-by":"publisher","first-page":"2015","DOI":"10.1103\/PhysRevLett.61.2015","article-title":"Model for a quantum hall effect without landau levels: condensed-matter realization of the parity anomaly","volume":"61","author":"Haldane","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib2","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1080\/00018732.2015.1068524","article-title":"Quantum anomalous Hall effect and related topological electronic states","volume":"64","author":"Weng","year":"2015","journal-title":"Adv. Phys."},{"key":"nanoad2483bib3","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1103\/RevModPhys.81.109","article-title":"The electronic properties of graphene","volume":"81","author":"Castro Neto","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"nanoad2483bib4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.146802","article-title":"Z 2 topological order and the quantum spin hall effect","volume":"95","author":"Kane","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.226801","article-title":"Quantum Spin hall effect in graphene","volume":"95","author":"Kane","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib6","doi-asserted-by":"publisher","first-page":"1757","DOI":"10.1126\/science.1133734","article-title":"Quantum spin hall effect and topological phase transition in HgTe quantum wells","volume":"314","author":"Bernevig","year":"2006","journal-title":"Science"},{"key":"nanoad2483bib7","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1126\/science.aai8142","article-title":"Bismuthene on a SiC substrate: a candidate for a high-temperature quantum spin Hall material","volume":"357","author":"Reis","year":"2017","journal-title":"Science"},{"key":"nanoad2483bib8","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1126\/science.aan6003","article-title":"Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal","volume":"359","author":"Wu","year":"2018","journal-title":"Science"},{"key":"nanoad2483bib9","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1038\/s41563-018-0203-5","article-title":"Epitaxial growth of ultraflat stanene with topological band inversion","volume":"17","author":"Deng","year":"2018","journal-title":"Nat. Mater."},{"key":"nanoad2483bib10","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1038\/s41586-018-0788-5","article-title":"Electric-field-tuned topological phase transition in ultrathin Na3Bi","volume":"564","author":"Collins","year":"2018","journal-title":"Nature"},{"key":"nanoad2483bib11","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1038\/nphys4174","article-title":"Quantum spin Hall state in monolayer 1T\u2032-WTe2","volume":"13","author":"Tang","year":"2017","journal-title":"Nat. Phys."},{"key":"nanoad2483bib12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.223901","article-title":"Scheme for achieving a topological photonic crystal by using dielectric material","volume":"114","author":"Wu","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib13","doi-asserted-by":"publisher","first-page":"24347","DOI":"10.1038\/srep24347","article-title":"Topological properties of electrons in honeycomb lattice with detuned hopping energy","volume":"6","author":"Wu","year":"2016","journal-title":"Sci. Rep."},{"key":"nanoad2483bib14","doi-asserted-by":"publisher","first-page":"16515","DOI":"10.1038\/s41598-017-16334-0","article-title":"Topological states characterized by mirror winding numbers in graphene with bond modulation","volume":"7","author":"Kariyado","year":"2017","journal-title":"Sci. Rep."},{"key":"nanoad2483bib15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.217401","article-title":"Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials","volume":"120","author":"Yang","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib16","doi-asserted-by":"publisher","first-page":"4598","DOI":"10.1038\/s41467-018-07084-2","article-title":"Topological LC-circuits based on microstrips and observation of electromagnetic modes with orbital angular momentum","volume":"9","author":"Li","year":"2018","journal-title":"Nat. Commun."},{"key":"nanoad2483bib17","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1126\/science.aaq0327","article-title":"A topological quantum optics interface","volume":"359","author":"Barik","year":"2018","journal-title":"Science"},{"key":"nanoad2483bib18","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.aaw4137","article-title":"Direct observation of topological edge states in silicon photonic crystals: spin, dispersion, and chiral routing","volume":"6","author":"Parappurath","year":"2020","journal-title":"Sci. Adv."},{"key":"nanoad2483bib19","doi-asserted-by":"publisher","first-page":"3040","DOI":"10.1038\/s41467-023-38325-8","article-title":"Unique huygens-fresnel electromagnetic transportation of chiral dirac wavelet in topological photonic crystal","volume":"14","author":"Wang","year":"2023","journal-title":"Nat. Commun."},{"key":"nanoad2483bib20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.236404","article-title":"Edge-dependent topology in kekul\u00e9 lattices","volume":"124","author":"Freeney","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib21","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1038\/nature10941","article-title":"Designer Dirac fermions and topological phases in molecular graphene","volume":"483","author":"Gomes","year":"2012","journal-title":"Nature"},{"key":"nanoad2483bib22","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1038\/nnano.2013.161","article-title":"Artificial honeycomb lattices for electrons, atoms and photons","volume":"8","author":"Polini","year":"2013","journal-title":"Nat. Nanotechnol."},{"key":"nanoad2483bib23","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1126\/science.aah6442","article-title":"Quantized electric multipole insulators","volume":"357","author":"Benalcazar","year":"2017","journal-title":"Science"},{"key":"nanoad2483bib24","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1038\/s41566-018-0179-3","article-title":"Topological protection of photonic mid-gap defect modes","volume":"12","author":"Noh","year":"2018","journal-title":"Nat. Photonics"},{"key":"nanoad2483bib25","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1038\/nature25156","article-title":"Observation of a phononic quadrupole topological insulator","volume":"555","author":"Serra-Garcia","year":"2018","journal-title":"Nature"},{"key":"nanoad2483bib26","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1038\/nature25777","article-title":"A quantized microwave quadrupole insulator with topologically protected corner states","volume":"555","author":"Peterson","year":"2018","journal-title":"Nature"},{"key":"nanoad2483bib27","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1038\/s41567-018-0246-1","article-title":"Topolectrical-circuit realization of topological corner modes","volume":"14","author":"Imhof","year":"2018","journal-title":"Nat. Phys."},{"key":"nanoad2483bib28","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1038\/s41563-018-0251-x","article-title":"Acoustic higher-order topological insulator on a kagome lattice","volume":"18","author":"Xue","year":"2019","journal-title":"Nat. Mater."},{"key":"nanoad2483bib29","doi-asserted-by":"publisher","first-page":"692","DOI":"10.1038\/s41566-019-0452-0","article-title":"Photonic quadrupole topological phases","volume":"13","author":"Mittal","year":"2019","journal-title":"Nat. Photonics"},{"key":"nanoad2483bib30","doi-asserted-by":"publisher","first-page":"1292","DOI":"10.1038\/s41563-019-0483-4","article-title":"Robust zero-energy modes in an electronic higher-order topological insulator","volume":"18","author":"Kempkes","year":"2019","journal-title":"Nat. Mater."},{"key":"nanoad2483bib31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.195416","article-title":"Counterpropagating topological interface states in graphene patchwork structures with regular arrays of nanoholes","volume":"98","author":"Kariyado","year":"2018","journal-title":"Phys. Rev. B"},{"key":"nanoad2483bib32","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1038\/nature09211","article-title":"Atomically precise bottom-up fabrication of graphene nanoribbons","volume":"466","author":"Cai","year":"2010","journal-title":"Nature"},{"key":"nanoad2483bib33","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1126\/science.aar2009","article-title":"Bottom-up synthesis of multifunctional nanoporous graphene","volume":"360","author":"Moreno","year":"2018","journal-title":"Science"},{"key":"nanoad2483bib34","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1351\/pac200880030519","article-title":"Synthesis and properties of annulenic subunits of graphyne and graphdiyne nanoarchitectures","volume":"80","author":"Haley","year":"2008","journal-title":"Pure Appl. Chem."},{"key":"nanoad2483bib35","doi-asserted-by":"publisher","first-page":"3256","DOI":"10.1039\/b922733d","article-title":"Architecture of graphdiyne nanoscale films","volume":"46","author":"Li","year":"2010","journal-title":"Chem. Commun."},{"key":"nanoad2483bib36","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1038\/s44160-022-00068-7","article-title":"Synthesis of \u03b3-graphyne using dynamic covalent chemistry","volume":"1","author":"Hu","year":"2022","journal-title":"Nat. Synth."},{"key":"nanoad2483bib37","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1038\/nature05180","article-title":"Half-metallic graphene nanoribbons","volume":"444","author":"Son","year":"2006","journal-title":"Nature"},{"key":"nanoad2483bib38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.216803","article-title":"Energy Gaps in Graphene Nanoribbons","volume":"97","author":"Son","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib39","doi-asserted-by":"publisher","DOI":"10.1063\/1.3583507","article-title":"Graphyne- and graphdiyne-based nanoribbons: density functional theory calculations of electronic structures","volume":"98","author":"Pan","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"nanoad2483bib40","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1038\/s41586-018-0376-8","article-title":"Topological band engineering of graphene nanoribbons","volume":"560","author":"Rizzo","year":"2018","journal-title":"Nature"},{"key":"nanoad2483bib41","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201909035","article-title":"The chemistry and promising applications of graphene and porous graphene materials","volume":"30","author":"Huang","year":"2020","journal-title":"Adv. Funct. Mater."},{"key":"nanoad2483bib42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.102.075444","article-title":"Optical excitations and thermoelectric properties of two-dimensional holey graphene","volume":"102","author":"Singh","year":"2020","journal-title":"Phys. Rev. B"},{"key":"nanoad2483bib43","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.3390\/nano11051074","article-title":"Holey graphene: topological control of electronic properties and electric conductivity","volume":"11","author":"Barkov","year":"2021","journal-title":"Nanomaterials"},{"key":"nanoad2483bib44","doi-asserted-by":"publisher","first-page":"4111","DOI":"10.1016\/j.carbon.2011.05.024","article-title":"Mechanical properties of graphyne","volume":"49","author":"Cranford","year":"2011","journal-title":"Carbon"},{"key":"nanoad2483bib45","doi-asserted-by":"publisher","first-page":"6492","DOI":"10.1021\/acs.nanolett.9b02719","article-title":"Two-dimensional quadrupole topological insulator in \u03b3-graphyne","volume":"19","author":"Liu","year":"2019","journal-title":"Nano Lett."},{"key":"nanoad2483bib46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.256402","article-title":"Two-dimensional second-order topological insulator in graphdiyne","volume":"123","author":"Sheng","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib47","doi-asserted-by":"publisher","first-page":"2306","DOI":"10.1016\/j.matt.2022.04.033","article-title":"Constructing two-dimensional holey graphyne with unusual annulative \u03c0-extension","volume":"5","author":"Liu","year":"2022","journal-title":"Matter"},{"key":"nanoad2483bib48","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1103\/RevModPhys.84.1419","article-title":"Maximally localized wannier functions: theory and applications","volume":"84","author":"Marzari","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"nanoad2483bib49","doi-asserted-by":"publisher","first-page":"11169","DOI":"10.1103\/PhysRevB.54.11169","article-title":"Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set","volume":"54","author":"Kresse","year":"1996","journal-title":"Phys. Rev. B"},{"key":"nanoad2483bib50","doi-asserted-by":"publisher","first-page":"1758","DOI":"10.1103\/PhysRevB.59.1758","article-title":"From ultrasoft pseudopotentials to the projector augmented-wave method","volume":"59","author":"Kresse","year":"1999","journal-title":"Phys. Rev. B"},{"key":"nanoad2483bib51","doi-asserted-by":"publisher","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized gradient approximation made simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib52","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2021.108033","article-title":"VASPKIT: a user-friendly interface facilitating high-throughput computing and analysis using VASP code","volume":"267","author":"Wang","year":"2021","journal-title":"Comput. Phys. Commun."},{"key":"nanoad2483bib53","doi-asserted-by":"publisher","first-page":"165902","DOI":"10.1088\/1361-648X\/ab51ff","article-title":"Wannier90 as a community code: new features and applications","volume":"32","author":"Pizzi","year":"2020","journal-title":"J. Phys.: Condens. Matter"},{"key":"nanoad2483bib54","doi-asserted-by":"publisher","first-page":"9123","DOI":"10.1038\/s41598-023-35016-8","article-title":"Colossal figure of merit and compelling HER catalytic activity of holey graphyne","volume":"13","author":"Sajjad","year":"2023","journal-title":"Sci. Rep."},{"key":"nanoad2483bib55","doi-asserted-by":"publisher","DOI":"10.7566\/JPSJ.88.104703","article-title":"Higher-order topological phase in a honeycomb-lattice model with anti-kekul\u00e9 distortion","volume":"88","author":"Mizoguchi","year":"2019","journal-title":"J. Phys. Soc. Jpn."},{"key":"nanoad2483bib56","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.196402","article-title":"Higher-order topological mott insulators","volume":"123","author":"Kudo","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"nanoad2483bib57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.012009","article-title":"ZQ Berry phase for higher-order symmetry-protected topological phases","volume":"2","author":"Araki","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"nanoad2483bib58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.89.224503","article-title":"Classification of two-dimensional topological crystalline superconductors and Majorana bound states at disclinations","volume":"89","author":"Benalcazar","year":"2014","journal-title":"Phys. Rev. B"},{"key":"nanoad2483bib59","doi-asserted-by":"publisher","first-page":"75119","DOI":"10.1103\/PhysRevB.84.075119","article-title":"Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection","volume":"84","author":"Yu","year":"2011","journal-title":"Phys. Rev. B"}],"container-title":["Nanotechnology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,14]],"date-time":"2025-06-14T14:52:05Z","timestamp":1749912725000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6528\/ad2483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,19]]},"references-count":59,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2024,2,19]]},"published-print":{"date-parts":[[2024,5,6]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6528\/ad2483","relation":{},"ISSN":["0957-4484","1361-6528"],"issn-type":[{"value":"0957-4484","type":"print"},{"value":"1361-6528","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,19]]},"assertion":[{"value":"Topological electronic states in holey graphyne","name":"article_title","label":"Article Title"},{"value":"Nanotechnology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2023-12-08","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-01-31","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-02-19","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}