{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:18:04Z","timestamp":1787789884729,"version":"build-2784847793"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T00:00:00Z","timestamp":1728518400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T00:00:00Z","timestamp":1728518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12141401"],"award-info":[{"award-number":["12141401"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Commun"],"DOI":"10.1038\/s41467-024-52992-1","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T14:04:02Z","timestamp":1728569042000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Relativistic artificial molecule of two coupled graphene quantum dots at tunable distances"],"prefix":"10.1038","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9622-8285","authenticated-orcid":false,"given":"Xiao-Feng","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Chen","family":"Zhuang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mo-Han","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Sheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5512-9608","authenticated-orcid":false,"given":"Qing-Feng","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5251-1687","authenticated-orcid":false,"given":"Lin","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,10,10]]},"reference":[{"key":"52992_CR1","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1038\/379413a0","volume":"379","author":"RC Ashoori","year":"1996","unstructured":"Ashoori, R. C. Electrons in artificial atoms. Nature 379, 413\u2013419 (1996).","journal-title":"Nature"},{"key":"52992_CR2","doi-asserted-by":"publisher","first-page":"1283","DOI":"10.1103\/RevModPhys.74.1283","volume":"74","author":"SM Reimann","year":"2002","unstructured":"Reimann, S. M. & Manninen, M. Electronic structure of quantum dots. Rev. Mod. Phys. 74, 1283\u20131342 (2002).","journal-title":"Rev. Mod. Phys."},{"key":"52992_CR3","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1080\/00018739300101484","volume":"42","author":"AD Yoffe","year":"1993","unstructured":"Yoffe, A. D. Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems. Adv. Phys. 42, 173\u2013262 (1993).","journal-title":"Adv. Phys."},{"key":"52992_CR4","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1063\/1.881393","volume":"46","author":"MA Kastner","year":"1993","unstructured":"Kastner, M. A. Artificial atoms. Phys. Today 46, 24\u201331 (1993).","journal-title":"Phys. Today"},{"key":"52992_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s11467-021-1125-2","volume":"17","author":"S-Y Li","year":"2021","unstructured":"Li, S.-Y. & He, L. Recent progresses of quantum confinement in graphene quantum dots. Front. Phys. 17, 33201 (2021).","journal-title":"Front. Phys."},{"key":"52992_CR6","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1103\/RevModPhys.23.69","volume":"23","author":"CCJ Roothaan","year":"1951","unstructured":"Roothaan, C. C. J. New developments in molecular orbital theory. Rev. Mod. Phys. 23, 69\u201389 (1951).","journal-title":"Rev. Mod. Phys."},{"key":"52992_CR7","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1126\/science.291.5503.451","volume":"291","author":"M Bayer","year":"2001","unstructured":"Bayer, M. et al. Coupling and entangling of quantum states in quantum dot molecules. Science 291, 451\u2013453 (2001).","journal-title":"Science"},{"key":"52992_CR8","doi-asserted-by":"publisher","first-page":"4043","DOI":"10.1103\/PhysRevLett.74.4043","volume":"74","author":"M Grundmann","year":"1995","unstructured":"Grundmann, M. et al. Ultranarrow luminescence lines from single quantum dots. Phys. Rev. Lett. 74, 4043\u20134046 (1995).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR9","doi-asserted-by":"publisher","first-page":"1792","DOI":"10.1126\/science.278.5344.1792","volume":"278","author":"G Schedelbeck","year":"1997","unstructured":"Schedelbeck, G., Wegscheider, W., Bichler, M. & Abstreiter, G. Coupled quantum dots fabricated by cleaved edge overgrowth: from artificial atoms to molecules. Science 278, 1792\u20131795 (1997).","journal-title":"Science"},{"key":"52992_CR10","doi-asserted-by":"publisher","first-page":"2601","DOI":"10.1002\/adma.200803109","volume":"21","author":"L Wang","year":"2009","unstructured":"Wang, L., Rastelli, A., Kiravittaya, S., Benyoucef, M. & Schmidt, O. G. Self-assembled quantum dot molecules. Adv. Mater. 21, 2601\u20132618 (2009).","journal-title":"Adv. Mater."},{"key":"52992_CR11","doi-asserted-by":"publisher","first-page":"1917","DOI":"10.1103\/PhysRevLett.79.1917","volume":"79","author":"W Wegscheider","year":"1997","unstructured":"Wegscheider, W., Schedelbeck, G., Abstreiter, G., Rother, M. & Bichler, M. Atomically precise GaAs\/AlGaAs quantum dots fabricated by twofold cleaved edge overgrowth. Phys. Rev. Lett. 79, 1917\u20131920 (1997).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR12","doi-asserted-by":"publisher","first-page":"1178","DOI":"10.1021\/acs.accounts.0c00691","volume":"54","author":"S Koley","year":"2021","unstructured":"Koley, S., Cui, J., Panfil, Y. E. & Banin, U. Coupled colloidal quantum dot molecules. Acc. Chem. Res. 54, 1178\u20131188 (2021).","journal-title":"Acc. Chem. Res."},{"key":"52992_CR13","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S1386-9477(98)00224-0","volume":"3","author":"W Wegscheider","year":"1998","unstructured":"Wegscheider, W., Schedelbeck, G., Bichler, M. & Abstreiter, G. Atomically precise quantum dots fabricated by two-fold cleaved edge overgrowth: from artificial atoms to molecules. Phys. E 3, 103\u2013111 (1998).","journal-title":"Phys. E"},{"key":"52992_CR14","doi-asserted-by":"publisher","first-page":"3699","DOI":"10.1021\/acs.nanolett.9b00772","volume":"19","author":"G Rodary","year":"2019","unstructured":"Rodary, G. et al. Real space observation of electronic coupling between self-assembled quantum dots. Nano Lett. 19, 3699\u20133706 (2019).","journal-title":"Nano Lett."},{"key":"52992_CR15","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/S0921-4526(98)00099-4","volume":"249\u2013251","author":"DG Austing","year":"1998","unstructured":"Austing, D. G., Honda, T., Muraki, K., Tokura, Y. & Tarucha, S. Quantum dot molecules. Phys. B: Condens. Matter 249\u2013251, 206\u2013209 (1998).","journal-title":"Phys. B: Condens. Matter"},{"key":"52992_CR16","doi-asserted-by":"publisher","first-page":"081311","DOI":"10.1103\/PhysRevB.72.081311","volume":"72","author":"L He","year":"2005","unstructured":"He, L., Bester, G. & Zunger, A. Electronic asymmetry in self-assembled quantum dot molecules made of identical InAs\/GaAs quantum dots. Phys. Rev. B 72, 081311 (2005).","journal-title":"Phys. Rev. B"},{"key":"52992_CR17","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1038\/27617","volume":"395","author":"TH Oosterkamp","year":"1998","unstructured":"Oosterkamp, T. H. et al. Microwave spectroscopy of a quantum-dot molecule. Nature 395, 873\u2013876 (1998).","journal-title":"Nature"},{"key":"52992_CR18","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1126\/science.1095452","volume":"304","author":"NJ Craig","year":"2004","unstructured":"Craig, N. J. et al. Tunable nonlocal spin control in a coupled-quantum dot system. Science 304, 565\u2013567 (2004).","journal-title":"Science"},{"key":"52992_CR19","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.1126\/science.1063182","volume":"293","author":"H Jeong","year":"2001","unstructured":"Jeong, H., Chang, A. M. & Melloch, M. R. The Kondo effect in an artificial quantum dot molecule. Science 293, 2221\u20132223 (2001).","journal-title":"Science"},{"key":"52992_CR20","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1126\/science.1071215","volume":"297","author":"AW Holleitner","year":"2002","unstructured":"Holleitner, A. W., Blick, R. H., H\u00fcttel, A. K., Eberl, K. & Kotthaus, J. P. Probing and controlling the bonds of an artificial molecule. Science 297, 70\u201372 (2002).","journal-title":"Science"},{"key":"52992_CR21","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-10814-z","volume":"7","author":"H Zheng","year":"2017","unstructured":"Zheng, H., Zhang, J. & Berndt, R. A minimal double quantum dot. Sci. Rep. 7, 10764 (2017).","journal-title":"Sci. Rep."},{"key":"52992_CR22","doi-asserted-by":"publisher","first-page":"4785","DOI":"10.1021\/acs.nanolett.8b01303","volume":"18","author":"L Banszerus","year":"2018","unstructured":"Banszerus, L. et al. Gate-defined electron\u2013hole double dots in bilayer graphene. Nano Lett. 18, 4785\u20134790 (2018).","journal-title":"Nano Lett."},{"key":"52992_CR23","doi-asserted-by":"publisher","first-page":"2005","DOI":"10.1021\/acs.nanolett.9b05295","volume":"20","author":"L Banszerus","year":"2020","unstructured":"Banszerus, L. et al. Single-electron double quantum dots in bilayer graphene. Nano Lett. 20, 2005\u20132011 (2020).","journal-title":"Nano Lett."},{"key":"52992_CR24","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/nnano.2014.129","volume":"9","author":"S F\u00f6lsch","year":"2014","unstructured":"F\u00f6lsch, S., Mart\u00ednez-Blanco, J., Yang, J., Kanisawa, K. & Erwin, S. C. Quantum dots with single-atom precision. Nat. Nanotechnol. 9, 505\u2013508 (2014).","journal-title":"Nat. Nanotechnol."},{"key":"52992_CR25","doi-asserted-by":"publisher","first-page":"076803","DOI":"10.1103\/PhysRevLett.115.076803","volume":"115","author":"Y Pan","year":"2015","unstructured":"Pan, Y., Yang, J., Erwin, S. C., Kanisawa, K. & F\u00f6lsch, S. Reconfigurable quantum-dot molecules created by atom manipulation. Phys. Rev. Lett. 115, 076803 (2015).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR26","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1126\/science.adf2685","volume":"380","author":"E Sierda","year":"2023","unstructured":"Sierda, E. et al. Quantum simulator to emulate lower-dimensional molecular structure. Science 380, 1048\u20131052 (2023).","journal-title":"Science"},{"key":"52992_CR27","doi-asserted-by":"publisher","first-page":"6738","DOI":"10.1021\/acs.nanolett.0c02623","volume":"20","author":"Z-Q Fu","year":"2020","unstructured":"Fu, Z.-Q. et al. Relativistic artificial molecules realized by two coupled graphene quantum dots. Nano Lett. 20, 6738\u20136743 (2020).","journal-title":"Nano Lett."},{"key":"52992_CR28","doi-asserted-by":"publisher","first-page":"076202","DOI":"10.1103\/PhysRevLett.130.076202","volume":"130","author":"Q Zheng","year":"2023","unstructured":"Zheng, Q. et al. Molecular collapse states in graphene\/WSe2 heterostructure quantum dots. Phys. Rev. Lett. 130, 076202 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR29","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1038\/s41565-023-01327-0","volume":"18","author":"Z Ge","year":"2023","unstructured":"Ge, Z. et al. Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules. Nat. Nanotechnol. 18, 250\u2013256 (2023).","journal-title":"Nat. Nanotechnol."},{"key":"52992_CR30","doi-asserted-by":"publisher","first-page":"4433","DOI":"10.1103\/PhysRevLett.84.4433","volume":"84","author":"B Partoens","year":"2000","unstructured":"Partoens, B. & Peeters, F. M. Molecule-type phases and Hund\u2019s rule in vertically coupled quantum dots. Phys. Rev. Lett. 84, 4433\u20134436 (2000).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR31","doi-asserted-by":"publisher","first-page":"2605","DOI":"10.1103\/PhysRevB.62.2605","volume":"62","author":"A Wensauer","year":"2000","unstructured":"Wensauer, A., Steffens, O., Suhrke, M. & R\u00f6ssler, U. Laterally coupled few-electron quantum dots. Phys. Rev. B 62, 2605\u20132613 (2000).","journal-title":"Phys. Rev. B"},{"key":"52992_CR32","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0038-1098(99)00305-1","volume":"112","author":"M Rontani","year":"1999","unstructured":"Rontani, M., Rossi, F., Manghi, F. & Molinari, E. Multiple quantum phases in artificial double-dot molecules. Solid State Commun. 112, 151\u2013155 (1999).","journal-title":"Solid State Commun."},{"key":"52992_CR33","doi-asserted-by":"publisher","first-page":"126401","DOI":"10.1103\/PhysRevLett.104.126401","volume":"104","author":"F Baruffa","year":"2010","unstructured":"Baruffa, F., Stano, P. & Fabian, J. Theory of anisotropic exchange in laterally coupled quantum dots. Phys. Rev. Lett. 104, 126401 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"52992_CR34","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-29251-2","volume":"13","author":"Q Zheng","year":"2022","unstructured":"Zheng, Q., Zhuang, Y.-C., Sun, Q.-F. & He, L. Coexistence of electron whispering-gallery modes and atomic collapse states in graphene\/WSe2 heterostructure quantum dots. Nat. Commun. 13, 1597 (2022).","journal-title":"Nat. Commun."},{"key":"52992_CR35","doi-asserted-by":"publisher","first-page":"L081408","DOI":"10.1103\/PhysRevB.108.L081408","volume":"108","author":"H-Y Ren","year":"2023","unstructured":"Ren, H.-Y., Ren, Y.-N., Zheng, Q., He, J.-Q. & He, L. Electron-electron interaction and correlation-induced two density waves with different Fermi velocities in graphene quantum dots. Phys. Rev. B 108, L081408 (2023).","journal-title":"Phys. Rev. B"},{"key":"52992_CR36","doi-asserted-by":"crossref","unstructured":"Ren, Y.-N. et al. In situ creation and tailoring of interfacial quantum dots in graphene\/transition metal dichalcogenide heterostructures. Phys. Rev. B 110, 125416 (2024).","DOI":"10.1103\/PhysRevB.110.125416"},{"key":"52992_CR37","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1038\/nphys1198","volume":"5","author":"AF Young","year":"2009","unstructured":"Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5, 222\u2013226 (2009).","journal-title":"Nat. Phys."},{"key":"52992_CR38","doi-asserted-by":"publisher","first-page":"1032","DOI":"10.1038\/nphys3805","volume":"12","author":"J Lee","year":"2016","unstructured":"Lee, J. et al. Imaging electrostatically confined Dirac fermions in graphene quantum dots. Nat. Phys. 12, 1032\u20131036 (2016).","journal-title":"Nat. Phys."},{"key":"52992_CR39","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1126\/science.aaa7469","volume":"348","author":"Y Zhao","year":"2015","unstructured":"Zhao, Y. et al. Creating and probing electron whispering-gallery modes in graphene. Science 348, 672\u2013675 (2015).","journal-title":"Science"},{"key":"52992_CR40","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1038\/nphys3806","volume":"12","author":"C Guti\u00e9rrez","year":"2016","unstructured":"Guti\u00e9rrez, C., Brown, L., Kim, C.-J., Park, J. & Pasupathy, A. N. Klein tunnelling and electron trapping in nanometre-scale graphene quantum dots. Nat. Phys. 12, 1069\u20131075 (2016).","journal-title":"Nat. Phys."},{"key":"52992_CR41","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1126\/science.aal0212","volume":"356","author":"F Ghahari","year":"2017","unstructured":"Ghahari, F. et al. An on\/off Berry phase switch in circular graphene resonators. Science 356, 845\u2013849 (2017).","journal-title":"Science"},{"key":"52992_CR42","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1038\/nnano.2017.181","volume":"12","author":"Y Jiang","year":"2017","unstructured":"Jiang, Y. et al. Tuning a circular p\u2013n junction in graphene from quantum confinement to optical guiding. Nat. Nanotechnol. 12, 1045\u20131049 (2017).","journal-title":"Nat. Nanotechnol."},{"key":"52992_CR43","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.97.045413","volume":"97","author":"K-K Bai","year":"2018","unstructured":"Bai, K.-K. et al. Generating atomically sharp p-n junctions in graphene and testing quantum electron optics on the nanoscale. Phys. Rev. B 97, 045413 (2018).","journal-title":"Phys. Rev. B"},{"key":"52992_CR44","doi-asserted-by":"publisher","first-page":"235310","DOI":"10.1103\/PhysRevB.101.235310","volume":"101","author":"Z-Q Fu","year":"2020","unstructured":"Fu, Z.-Q., Bai, K.-K., Ren, Y.-N., Zhou, J.-J. & He, L. Coulomb interaction in quasibound states of graphene quantum dots. Phys. Rev. B 101, 235310 (2020).","journal-title":"Phys. Rev. B"},{"key":"52992_CR45","doi-asserted-by":"publisher","unstructured":"Moldovan, D. & Peeters, F. pybinding v0.9.5: a Python package for tight-binding calculations. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.4010216 (2020).","DOI":"10.5281\/zenodo.4010216"},{"key":"52992_CR46","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1103\/RevModPhys.78.275","volume":"78","author":"A Wei\u00dfe","year":"2006","unstructured":"Wei\u00dfe, A., Wellein, G., Alvermann, A. & Fehske, H. The kernel polynomial method. Rev. Mod. Phys. 78, 275\u2013306 (2006).","journal-title":"Rev. Mod. Phys."},{"key":"52992_CR47","doi-asserted-by":"publisher","first-page":"167006","DOI":"10.1103\/PhysRevLett.105.167006","volume":"105","author":"L Covaci","year":"2010","unstructured":"Covaci, L., Peeters, F. M. & Berciu, M. Efficient numerical approach to inhomogeneous superconductivity: the Chebyshev-Bogoliubov\u2013de Gennes method. Phys. Rev. Lett. 105, 167006 (2010).","journal-title":"Phys. Rev. Lett."}],"container-title":["Nature Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-52992-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-52992-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-52992-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T16:05:27Z","timestamp":1728576327000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-52992-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,10]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["52992"],"URL":"https:\/\/doi.org\/10.1038\/s41467-024-52992-1","relation":{},"ISSN":["2041-1723"],"issn-type":[{"value":"2041-1723","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,10]]},"assertion":[{"value":"17 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"8786"}}