Abstract
We consider the gapped graphene superlattice (SL) constructed in accordance with the Fibonacci rule. The value of a gap is assumed to be equal in all SL elements and we propose to create the quasi-periodic modulation due to the difference in values of the barrier height in different SL elements. It is shown that the effective splitting of the allowed bands and thereby forming a series of gaps is realized under the normal incidence of electrons on the SL. Energy spectra reveal a periodical character on the whole energy scale. The splitting of allowed bands is subjected to the Fibonacci inflation rule. The gap associated with the new Dirac point is formed in every Fibonacci generation. Both the location and the width of this gap are dependent on the barrier heights. Results obtained allow for controlling the energy spectra of the graphene-based SLs and may be useful for operating the nano-electronic devices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tsu R (2011) Superlattice to nanoelectronics, 2nd edn. Elsevier, Oxford327 p
Cheng Z, Savit R, Merlin R (1988) Structure and electronic properties of Thue-Morse lattices. Phys Rev B 37:4375
Geim AK, Novoselov KS (2007) The rise of graphene. Nat Materials 6:183
Castro Neto AN, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of graphene Rev Mod Phys 81:109
Pereira JM, Peeters FM, Chaves A, Farias, GA (2010) Klein tunneling in single and multiple barriers in graphene Semicond Sci Tech 25:033002
Cheianov VV, Falko VI (2006) Selective transmission of Dirac electrons and ballistic magnetoresistance of n-p junctions in graphene Phys Rev B 74:041403
Zhao Q, Gong J, Muller CA (2012) Localization behavior of Dirac particles in disordered graphene superlattices Phys Rev B 85:104201
Barbier M, Vasilopoulos P, Peeters FM (2011) Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines E-print archives, cond-mat/1101.4117 V 1
Wang L, Chen X (2010) Robust zero-averaged wave-number gap inside gapped graphene superlattices E-print archives, cond-mat. Mes-hall/1008. 0504, V 1
Wang L, Zhu S (2010) Electronic band gaps and transport properties in graphene superlattices with one-dimensional periodic potentials of square barriers Phys Rev B 81:205444
Nhuyen VH, Bournel A, Dollfus P (2011) Resonant tunneling structures based on epitaxial graphene on SiC Semicond Sci Technol 26:125012
Barbier M, Vasilopoulos P, Peeters FM (2009) Dirac electrons in a Kronig-Penney potential: Dispersion relation and transmission periodic in the strength of the barriers Phys Rev B 80:205415
Zhao P, Chen X (2011) Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice E-print archives, cond-mat. Mes-hall/1111. 1754 V 1
Ma T, Liang C, Wang L, Chen X (2011) E-print archives, cond-mat. 1754 V 1
Bliokh YuP, Freilikher V, Savel’ev S, Nori F (2009) Transport and localization in periodic and disordered graphene superlattices Phys Rev B 79:075123
Ratnikov PV (2009) Superlattice based on graphene on a strip substrate JETP Lett 90(6):469
Meyer JC, Girit CO, Crommie MF, Zetti A Hydrocarbon lithography on graphene membranes (2008) Appl Phys Lett 92:123110
Sutter PW, Flege J, Sutter EA (2008) Epitaxial graphene on ruthenium. Nat Materials 7:406
Coraux J, N’Diaye AT, Busse C, Micheli T (2008) Structural coherency of graphene on Ir(111). Nano Lett 8:565
Son YW, Cohen ML, Louie SG (2006) Energy gaps in graphene nanoribbons. Phys Rev Lett 97:216803
Han MY, Ozyilmaz B, Zhang Y, Kim F (2007) Energy band-gap engineering of graphene nanoribbons. Phys Rev Lett 98:206805
Giovanetti G, Khomyakov PA, Brocks G, Kelly P, van der Brink J (2007) Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations Phys Rev B 76:073103
Zhou SY, Gweon G, Fedorov AV, Guinea F, Castro Neto AH, Lanzara A, First P, de Heer W, Lee D-H (2007) Substrate-induced bandgap opening in epitaxial graphene. Nat Materials 6:770
Balog R, Jorgensen B, Nilsson L, Anderson M, Rienks E, Bianchi M (2010) Bandgap opening in graphene induced by patterned hydrogen adsorption. Nat Materials 9:315
Casolo S, Martinazzo R, Tantardini GF (2011) Band Engineering in Graphene with Superlattices of Substitutional Defects J Phys Chem C 115(8):3250
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Korol, A., Isai, V. (2015). Energy Spectra of the Fibonacci Superlattice Based on the Gapped Graphene. In: Fesenko, O., Yatsenko, L. (eds) Nanocomposites, Nanophotonics, Nanobiotechnology, and Applications. Springer Proceedings in Physics, vol 156. Springer, Cham. https://doi.org/10.1007/978-3-319-06611-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-06611-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06610-3
Online ISBN: 978-3-319-06611-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)