content_image/436656.jpg
Fig.10. The properties of these states are given in Refs.[6, 11, 12, 31, 32]: LLL states of valley K (K ′ ) are of B (A) type and localized surface states have a mixed character between A and B. The surface states can have various localization lengths but the minimum value is of order the carbon-carbon distance a$_{0}$ [12]. The arm- chair edges couple K and K ′ valleys[6, 11, 26], and, con- sequently, surface and LLL states of a nanoribbon can be coupled and give rise to mixed states with significant weight on the zigzag edges and inside the dot, as shown in Fig.6(c) and Fig.7(c). In addition, these mixed states should display a significant occupation of both A and B 

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<img src='content_image/436656.jpg'>

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This work was supported by the Korea Research Foun- dation Grant funded by the Korean Government (KRF- 2009-0074470). In addition this work was supported by the Second Brain Korea 21 Project. 

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## Acknowledgments 

