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In this article, we present a detailed C\u2013K phase diagram, constructed using the crystal structure prediction method, MAGUS, based on machine-learning potentials fitted from first-principles calculations, revealing diverse carbon units, from allylenide ions to graphene-like two-dimensional layers. We found that the Pnma C12K16 phase contains allylenide ions, which contribute to its insulating behavior. Meanwhile, the ambient-pressure stable Cmcm C12K4 phase contains potassium-intercalated carbon layers with unique pentagonal\u2013hexagonal\u2013heptagonal (5\u20136\u20137) carbon rings, which we term \u201c\u03c3-graphene.\u201d This \u03c3-graphene monolayer can be synthesized either by exfoliating bulk C12K4 using an electrochemical method or by removing potassium atoms via evaporating. Furthermore, Boltzmann transport calculations show that pristine \u03c3-graphene exhibits a high electrical conductivity (\u223c5.5 \u00d7 107 S\/m at 300\u00a0K), comparable with silver and copper, making it a promising material for electrical transport applications. In addition, \u03c3-graphene demonstrates excellent adsorption capabilities for O2 and NO2, with adsorption energies of \u22120.503 and \u22120.528\u00a0eV, respectively, suggesting potential applications in catalysis and environmental monitoring. Our work highlights the C\u2013K system as a versatile platform for synthesizing and applying novel carbon-based materials.<\/jats:p>","DOI":"10.1063\/5.0310376","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T13:02:27Z","timestamp":1766494947000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Diverse carbon units in high-pressure C\u2013K system predicted from first-principles and machine-learning methods"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2907-8149","authenticated-orcid":false,"given":"Qing","family":"Lu","sequence":"first","affiliation":[{"name":"School of Physics and Electrical Information, Jiangsu Second Normal University 1 , Nanjing 210013,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8669-7500","authenticated-orcid":false,"given":"Zhongwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yijie","family":"Zhu","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2278-7652","authenticated-orcid":false,"given":"Chi","family":"Ding","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-1106-3658","authenticated-orcid":false,"given":"Xiaomeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University 3 , Yinchuan 750021,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjie","family":"Wang","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Han","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6172-9100","authenticated-orcid":false,"given":"Jian","family":"Sun","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University 2 , Nanjing 210093,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,12,23]]},"reference":[{"key":"2025122308022119300_c1","doi-asserted-by":"publisher","first-page":"6437","DOI":"10.1039\/c7tb00891k","article-title":"Carbon nanostructures in biology and medicine","volume":"5","year":"2017","journal-title":"J.\u00a0Mater. 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