Band Structure and Spatial Localization of Electrons in Twisted Bilayer Graphene Nanoribbons
DOI:
https://doi.org/10.48165/Keywords:
Band Structure, Saptial localization, twisted bilayer, nanoribbon, chiral graphene, energy dispersion, splitting edge band, Dirac PointAbstract
We have studied the band structure, density of states and spatial localization of electron in twisted bilayer nanoribbons by means of tight binding calculation. In Chiral geometries, edge states are also related to the presence of zig-zag edge atoms, although they presented remarkable size effects. Physical properties of chiral graphene nanoribbons and general edges can have a stong dependence on chirality. We have analysed the properties of edge states in twisted bilayaer ribbons, explaining their energy dispersion and spatial localization. The different splittings were found in edge bands due to the inhomogeneous interplay coupling. For stacked zig-zag atoms the coupling was larger than corresponding edge states splitted apart, but edge states stemming from regions with stacking, where the interlayer coupling was smaller and gave rise to zero energy bands. We have also been found that in the edge regions where top and bottom zig-zag terminations were stacked, inter-ribbon tunneling between the dispersions less zero energy states created bonding and antibonding combination with energies away from the energy of the Dirac point. The obtained results were found in good agreement with previously obtained results.
References
Trambly. G. De Laissardiere, Mayon. D and Magand. L., (2010), Nano. Lett. 10, 804. [2] Morell. E. Suanrez., Borrea. J. D., Vargas. P, Pacheco. M, ABarticevic. Z, (2010), Phys. Rev. B, 82, 121407.
Trambly. G. De Laissar Diere et al., (2012), Phys. Rev. B, 86, 125413.
Li. G, Luican. A, Lopes. J. M. B. dossantos, Castro. Neto. A.H, Reina. A, Kong. J. and Ander E.Y., (2010), Nat. Phys. 6, 109.
Yan. W., Liu. M., Dou. R. F., Meng. L, Feng. L, Chu. Z. D., Zhang. Y, Liu. Z., Nie. J. C. and He. L., (2012), Phys. Rev. Lett. 109, 126801.
Sato. K, Saito. R, Cong. C, Yu. T., and Dresselhaus. M. S., (2012), Phys. Rev. B, 86, 125414.
Kim. K, Coh. S., Tan. L-Z, Regan. W, Yuk. J. M., Laie. S. G., Chatterjee. E, Crommee. M. F., Cohen. M. L. and Zettl. A, (2012), Phys. Rev. Lett. 108, 246103.
Varchon. F, Mallet. P, Magaud. L. and Venillen. J. Y., (2008), Phys. Rev. B, 77, 165415.
Kosynkin. D. V., Higginbotham, A. L. Sinitski. A, Lomeda. J. R., Dimiev. A., Price. B. K. and Tour. J. M., (2009), Nature (London), 458, 872.
Jiao. L., Zhang. L., Wang. X., Diaakiv. G. and Dai. H, (2009), Nature (London), 458, 877. [11]Xie. L, Wang. H, Jin. C, Wnag. X, Jiao. L,
Suenaga. K and Dai.H, (2011), J. Am Chem. Soc. 133, 10394.
Akhmerov. A. R. and Beenakker. C. W. J, (2008), Phys. Rev. B, 77, 085423.
Jaskolski. W, Aynela. A, Pele. M, Santos. H, and Chico. L, (2011), Phys. Rev. B, 83, 235424.
Nakada. K, Fujita. M, Dresselhaus. G and Dresselhaus. M. S, (1996), Phys. Rev. B, 54, 17954.
Brey. L and Fertig. H. A., (2006), Phys. Rev. B, 73, 235411.
Lopes. J. M. B., Dos Santos, Peres. N. M. R. and Castro. A.H. Neto, (2007), Phys. Rev. Lett. 99, 256802.
Shallcross. S, Sharma. S and Pankratov. O. A., (2008), Phys. Rev. Lett. 101, 056803. [18]Shallcross. S, Sharma. S, Kaneiaki. E and Pankrativ. O. A, (2010), Phys. Rev. B, 81, 165105.
Bistritzer. R and Mac Donald. A. H, (2011), Proc. Natl. Acad. Sci, U. S. A., 108, 12233. [20]Lopes. J. M. B. dos santos, Peres. N. M. R. and Castro. A. H. Neta, (2012), Phys. Rev. B, 86 155449.
San-Jose. P, Gonzaliz. J and Guinea. F, (2012), Phys. Rev. Lett. 108, 216802.
Morell. E. Sunarez, Pacheco. M, Chico. L and Breyy. L. B, (2013) Phys. Rev. B, 87, 125414.
Stauber. T, San-Jose. P and Brecy. L, (2013), New. J. Phys. 15, 113050.
Correa. J. D, Pacheco. M and Morell. E. Suarez, (2014), J. Mater. Sc. 49, 642.
Luican. A, Li. G, Eeina. A, Kong. J. Nair. R. R, Novoselov. K. S, Geim. A. K and Andrei. E. Y, (2011), Phys. Rev. Lett. 106, 126802.
Brihuega. I et al, (2012), Phys. Rev. Lett. 109, 196802.
Xian. L, Barraza. Lopez-S and Chou. M. Y, (2011), Phys. Rev. B, 84, 075425.
Morell. E. Suarez, Vargas. P et al, (2014), Phys. Rev. B, 84, 195421.
Singh Kumar Ashok, Ahmad Ali and Jagriti, (2017), B. P. A. S. Phys. No-1, 36D, 75. [30]Mishra. A and Kumar. A, (2021), B. P. A. S., 40D, Phy. No-1, 44.
