@article{b637f97b6b7b48cf8d1cbc1ca6645289,
title = "Low-energy Landau levels of Bernal zigzag graphene ribbons",
abstract = "Low-energy Landau levels of Bernal zigzag graphene ribbons in the presence of a uniform perpendicular magnetic field (B) are investigated by the Peierls coupling tight-binding model. State energies and associated wave functions are dominated by the B -field strength and the kz -dependent inter-ribbon interactions. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level. Many doubly degenerate Landau levels and singlet curving magnetobands exist along the kx and kz directions, respectively. The kz -dependent inter-ribbon interactions dramatically modify the magnetobands, such as the lift of double degeneracy, the change in state energies, and the production of two groups of curving magnetobands. They also change the characteristics of the wave functions and cause the redistribution of the charge-carrier density. The kz -dependent wave functions are further used to predict the selection rule of the optical transition.",
author = "Huang, {Y. C.} and Chang, {C. P.} and Su, {W. S.} and Lin, {M. F.}",
note = "Funding Information: This work was supported by the Taiwan National Science Council (Grant Nos. NSC 96-2112-M-165-001 MY3 and NSC 95-2112-M-006-0002). FIG. 1. (a) The geometric structure of the N y = 3 Bernal zigzag graphene nanoribbons. (b) γ 0 = 2.598 eV is the intralayer interaction. γ 1 = 0.364 eV ( γ 5 = 0.036 eV ) represents the interaction between two A atoms from two neighboring ribbons (two next-neighboring ribbons), and γ 3 = 0.319 eV ( γ 2 = − 0.014 eV ) is for B atoms. γ 4 = 0.177 eV corresponds to the inter-ribbon interaction between A atoms and B atoms. γ 6 = − 0.026 eV is the chemical shift between A atoms and B atoms. The values of γ i are the same as those of Bernal graphite (Ref. 38 ). FIG. 2. The k x -dependent low-energy bands for the Bernal zigzag graphene ribbons with (a) N y = 3000 at B = 0 , (b) N y = 3000 at B = 20 T , (c) N y = 3000 at B = 10 T , and (d) N y = 6000 at B = 20 T . [(e)–(h)] Same plot as (a)–(d) but for the k z dependence. FIG. 3. (a) Landau plot of the N y = 3000 ribbon at k z I z = π / 2 . (b) The Landau-level energies of the N y = 3000 ribbon at k z I z = π / 2 vs B . (c) Landau plot of the N y = 3000 ribbon at k z = 0 . (d) The relation between Landau-level energies of the N y = 3000 ribbon at k z = 0 and B . FIG. 4. The envelope functions for the Bernal zigzag graphene ribbons N y = 3000 subjected to B = 20 T at k z I z = π / 2 , 0.499 π , 0.4 π , and 0 are shown, respectively, in (a)–(d). FIG. 5. (a) The energy dispersions of the n = 1 and n ¯ = 0 subbands. (b) The variation of the envelope functions, related to the n = 1 and n ¯ = 0 subbands, with k z I Z . ",
year = "2009",
doi = "10.1063/1.3159643",
language = "English",
volume = "106",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "1",
}