{"title":"A New Graph Theory to Unravel the Bulk-Boundary Correspondence of Graphene Nanoribbons","authors":"Cheng-Hao Lu, Elise Yu-Tzu Li","doi":"10.1016/j.carbon.2024.119624","DOIUrl":null,"url":null,"abstract":"<p>We developed a new graph theory rooted in Clar's sextet rule to unravel the bulk boundary correspondence of graphene. This methodology is specifically focused on the topological invariant and the chiral winding number, which enables the chemical rationalization of edge and boundary states in one-dimensional graphene nanoribbon (GNR) materials. The Clar structure derived from facile Lewis structures facilitates direct prediction of free radical distribution along edges and boundaries of GNRs across various geometric configurations. We then extend this graph theoretical framework to include metallic GNRs, demonstrating its power in several paradigms where conventional topological theories show limitations. Upon reducing the topological parameters and hence the complexity, the new approach provides a visual comprehension for the electronic topology and hence conductivity of GNR, greatly simplifying the formulation of design principles for future application of graphene interconnects.</p>","PeriodicalId":262,"journal":{"name":"Carbon","volume":null,"pages":null},"PeriodicalIF":10.5000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carbon","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1016/j.carbon.2024.119624","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We developed a new graph theory rooted in Clar's sextet rule to unravel the bulk boundary correspondence of graphene. This methodology is specifically focused on the topological invariant and the chiral winding number, which enables the chemical rationalization of edge and boundary states in one-dimensional graphene nanoribbon (GNR) materials. The Clar structure derived from facile Lewis structures facilitates direct prediction of free radical distribution along edges and boundaries of GNRs across various geometric configurations. We then extend this graph theoretical framework to include metallic GNRs, demonstrating its power in several paradigms where conventional topological theories show limitations. Upon reducing the topological parameters and hence the complexity, the new approach provides a visual comprehension for the electronic topology and hence conductivity of GNR, greatly simplifying the formulation of design principles for future application of graphene interconnects.
期刊介绍:
The journal Carbon is an international multidisciplinary forum for communicating scientific advances in the field of carbon materials. It reports new findings related to the formation, structure, properties, behaviors, and technological applications of carbons. Carbons are a broad class of ordered or disordered solid phases composed primarily of elemental carbon, including but not limited to carbon black, carbon fibers and filaments, carbon nanotubes, diamond and diamond-like carbon, fullerenes, glassy carbon, graphite, graphene, graphene-oxide, porous carbons, pyrolytic carbon, and other sp2 and non-sp2 hybridized carbon systems. Carbon is the companion title to the open access journal Carbon Trends. Relevant application areas for carbon materials include biology and medicine, catalysis, electronic, optoelectronic, spintronic, high-frequency, and photonic devices, energy storage and conversion systems, environmental applications and water treatment, smart materials and systems, and structural and thermal applications.