References
1. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D.,
Zhang, Y., Dubons, S.V., Grigorieva, I.V., and Firsov,
A.A. \Electric Field in atomically thin carbon lms",
Science, 306(3), pp. 666-670 (2004).
2. Geim, A.K. and Novoselov, K.S. \The rise of
graphene", Nature Mater, 6(2), pp. 183-188 (2007).
3. Balandin, A.A., Ghosh, S., Bao, W., Calizo, I.,
Teweldebrhan, D., Miao, F., and Lau, C.N. \The
electric thermal conductivity of graphene", Nano Lett
8(2), pp. 902-907 (2008).
4. Ohta, T., Bostwick, A., Seyller, T., Horn, K., and
Rorenberg, E. \Controlling the electronic structure
of bilayer graphene", Science, 313(2), pp. 951-955
(2006).
5. Katsnelson, M.I., Novoselov, K.S., and Geim, A.K.
\Chiral tunneling and the Klein paradox in graphene",
Nat. Phys, 2(1), pp. 620-925 (2006).
6. Zhang, Y., Tan, T.-W., Stormer, H.L., and Kim,
P. \Experimental observation of the quantum Hall
e ect and Berry phase in graphene", Nature, (London),
438(2), pp. 201-205 (2005).
H. Rezania et al./Scientia Iranica, Transactions F: Nanotechnology 25 (2018) 1808{1814 1813
7. Bolotin, K.I., Sikes K.J., Jiang, Z., Klima, M., Fudenberg,
G., Hone, J., Kim, P., and Stormer, H.L.
\Ultrahigh electron mobility in suspended graphene",
Solid State Commun, 146(2), pp. 351-356 (2008).
8. Fujita, M., Wakabayashi, K., Nakada, K., and Kusakabe,
K. \Peculiar localized state at zigzag graphite
edge", J. Phys. Soc. Jpn, 65(2) pp. 1920-1927 (1996).
9. Nakada, K., Fujita, M., Dresselhaus, G., and Dresselhaus,
M.S. \Graphene nanoelectronics: Metrology,
Synethesis", Phys. Rev. B, 54(2), pp. 17954-17959
(1996).
10. Ezawa, M. \Peculiar phase dependence of the electronic
properties of carbon nanoribbons", Phys. Rev.
B, 73(3), pp. 045432-045438 (2006).
11. Berger, C. \Ultrathin epitaxial graphite: 2D electron
gas properties", J. Phys. Chem. B, 108(2), pp. 19912-
19917 (2004).
12. Areshkin, D.A. and White, C.T. \Ballistic transport
in graphene nanostrips in the graphene", Nano Lett,
7(3) pp. 204-208 (2007).
13. Sols, F., Guinea, F., and Castro, Neto, A.H. \Coulomb
blockade in graphene nanoribbons", Phys. Rev. Lett,
99(2), pp. 166803-166809 (2007).
14. Novikov, D.S. \Transverse eld e ect in graphene
ribbons", Phys. Rev. Lett, 99(3), pp. 056802-056805
(2007).
15. Kane, C.L. and Male, E.J. \Size, shape and low energy
electronic structure of carbon nanotubes", Phys. Rev.
Lett, 78(3), pp. 1932-1935 (1997).
16. Van Tuan, D., Marmolejo-Tejada, J.M., Waintal, X.,
Nikolic, B.K., Valenzuela, S.O., and Roche, S. \Spin
hall e ect and origins of nonlocal resistance in adatomdecorated
graphene", Phys Rev Lett, 117, pp. 176602-
176605 (2016).
17. Wakabayashi, K., Sigrist, M., and Fujita, M. \Role
of edges in the electronic and magnetic structures of
nanographene", J. Phys. Soc. Japan, 67(2), pp. 2089-
2095 (1998).
18. Saroka, V.A., Shuba, M.V., and Portnoi, M.E. \Optical
selection rules of zigzag graphene nanoribbons",
Phys. Rev. B, 95, pp. 155438-155445 (2017).
19. Chung, H.-C., Chang, C.-P., Lin, C.-Y., and Lin,
M.-F. \Electronic and optical properties of graphene
nanoribbons in external elds", Phys. Chem. Chem.
Phys, 18, pp. 7573-7580 (2016).
20. Sasaki, K., Murakami, S., and Saito, R. \Gauge eld
for edge state in graphene", J. Phys. Soc. Jpn, 75(3),
pp. 074713-074720 (2006).
21. Sasaki, K., Murakami, S., and Saito, R. \Stabilization
mechanism of edge state in graphene", Appl. Phys.
Lett, 88(3), pp. 113110-113117 (2006).
22. Brey, L., Fertig, H.A., and Das Sarma, S. \Dilute
graphene antiferromagnet", Phys. Rev. Lett, 99(2), pp.
116802-116805 (2007).
23. Marconcini, P. and Macucci, M. \The k.p method
and its application to graphene, carbon nanotubes and
graphene nanoribbons: the Dirac equation", La Rivista
del Nuovo Cimento, 34(8-9), pp. 489-584 (2011).
24. Brey, L. and Fertig, H.A. \Electronic states of
graphene nanoribbons studied with the Dirac equation",
Phys. Rev. B, 73(2), pp. 235411-235417 (2006).
25. Zheng, H., Wang, Z.F., Luo, T., Shi, Q.W., and
Chen, J. \Analytical study of electronic structure in
armchair graphene nanoribbons", Phys. Rev. B, 75(2),
pp. 165414-165420 (2007).
26. Ajiki, H. and Ando, T. \Electronic states of carbon
nanotubes", J. Phys. Soc. Jpn, 62, pp. 1255-1260
(1993).
27. Blankenburg, S., Cai, J., Rueux, P., Jaafar, R.,
Passerone, D., Feng, X., Mllen, K., Fasel, R., and
Pignedoli, C.A. \Intraribbon heterojunction formation
in ultranarrow graphene nanoribbons", ACS Nano,
6(3), pp. 2020-2028 (2012).
28. Rueux, P., Cai, J., Pumb, C.N., Patthey, L., Prezzi,
D., Ferretti, A., Molinari, E., Feng, X., Mllen, K.,
Pignedoli, C.A., and Fasel, R. \Electronic structure of
atomically precise graphene nanoribbons", Acs Nano,
6(3), pp. 6930-6937 (2012)
29. Rezania, H. and Abdi, A. \Dynamical and static spin
susceptibilities of doped gapped graphene nanoribbon
due to local electronic interaction", Plasmonics, 13(3),
pp. 845-854 (2018).
30. Wakabayashi, K., Sasaki, K.-H., Nakanishi, T., and
Enoki, T. \Electronic states of gapped nanoribbons
and analytical solutions", Science and Technology of
Advanced Materials, 11(5), pp. 1-18 (2010).
31. Mahan, G.D., In Many Particle Physics, 3rd Ed., pp.
295-331, Plenum Press, New York (1993).
32. Paul, I. and Kotliar, G. \Thermal transport for many
body tight binding models", Phys. Rev. B, 67(2), p.
115131 (2003).
33. Deng, H.-Y., Wakabayashi, K., and Lam, C.-H.
\Mode-Matching approach to current blocking e ect
in graphene nanoribbons", J. Phys. Soc. Japan, 82,
pp. 104707-104717 (2013).
34. Deng, H.-Y. and Wakabayashi. K. \Edge e ect on a
vacancy state in semi-in nite graphene", Phys. Rev.
B, 90, pp. 115413-115420 (2014).
35. Luck, J.M. and Avishai, Y. \Unusual electronic properties
of clean and disordered zigzag graphene nanoribbons",
J. Phys. Condens. Matter, 27, pp. 025301-
025310 (2015).
1814 H. Rezania et al./Scientia Iranica, Transactions F: Nanotechnology 25 (2018) 1808{1814
36. Rezania, H. \Electrical conductivity of zigzag carbon
nanotubes including Holstein polarons", European
Physical Journal B, 85, pp. 1-5 (2012).
37. Mousavi, H. and Bagheri, M. \E ect of Holstein
phonons on the electrical conductivity of carbon nanotubes",
Physica E, 44, pp. 1722-1724 (2012).
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