Determining the defect type in a graphene lattice

Abstract

AbstractWe consider four common defects that appear in an infinite single-layer graphene lattice, i.e. single vacancy V1(5−9), Stone-Wales SW (55−77), and double vacancies V2(5−8−5) and V2(555−777). Investigating the honeycomb pattern of the graphene, we make use of the concept of shortest closed paths (periodic orbits) in the underlying topological structure. Using properties of the shortest closed paths of odd length we present and prove mathematically an algorithm that classifies which one of these defects occurs.Keywords: Grapheneinverse problemsingle vacancy defectdouble vacancy defectStone-WalesMATHEMATICS SUBJECT CLASSIFICATION (2020): 47N6081Q1034A5534B45 Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work was supported by the National Research Foundation of South Africa under grant no.s 89147 and 103530.