Journal
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
Volume 79, Issue 3, Pages -Publisher
PHYSICAL SOC JAPAN
DOI: 10.1143/JPSJ.79.034706
Keywords
graphene; edge states; flat bands; graphene nanoribbons; Dirac equation; transfer matrix; valley polarization; magnetism
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Funding
- Ministry of Education, Culture, Sports, Science and Technology [19710082, 19310094, 20001006]
- Japan Society for the Promotion of Science
- Grants-in-Aid for Scientific Research [19710082] Funding Source: KAKEN
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We study the electronic states of graphene nanoribbons with modified edge structures by attaching Klein's bearded bonds as a minimal model of edge modification. The partial attachment of Klein's bearded bonds to graphene nanoribbons gives rise to the partial flat bands at zero-energy even under the condition of vertical bar N-A - N-B vertical bar = 0, where N-A (N-B) is the number of A (B)-sublattice sites. Using transfer matrix method, we successfully derive the analytic representation of edge states for modified zigzag edge. The modification of armchair edges causes the complete flat bands, where the wavefunction has the character of valley polarization. We also applied the density functional theory to optimize the lattice structure and estimate the spin density. Our results indicate that the chemical and structural modification of graphene edge will serve to design and stabilize the spin polarized edge states.
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