Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

被引:21
作者
Brun, S. J. [1 ]
Thomsen, M. R.
Pedersen, T. G.
机构
[1] Aalborg Univ, Dept Phys & Nanotechnol, Skjernvej 4A, DK-9220 Aalborg, Denmark
基金
新加坡国家研究基金会;
关键词
graphene; antidot lattice; band gap; Dirac equation; ZIGZAG;
D O I
10.1088/0953-8984/26/26/265301
中图分类号
O469 [凝聚态物理学];
学科分类号
070205 ;
摘要
The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation ( DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding ( TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.
引用
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页数:8
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共 34 条
[1]   Ultrahigh electron mobility in suspended graphene [J].
Bolotin, K. I. ;
Sikes, K. J. ;
Jiang, Z. ;
Klima, M. ;
Fudenberg, G. ;
Hone, J. ;
Kim, P. ;
Stormer, H. L. .
SOLID STATE COMMUNICATIONS, 2008, 146 (9-10) :351-355
[2]   Electronic states of graphene nanoribbons studied with the Dirac equation [J].
Brey, L ;
Fertig, HA .
PHYSICAL REVIEW B, 2006, 73 (23)
[3]   Bandgap Opening by Patterning Graphene [J].
Dvorak, Marc ;
Oswald, William ;
Wu, Zhigang .
SCIENTIFIC REPORTS, 2013, 3
[4]   Weak localization and transport gap in graphene antidot lattices [J].
Eroms, J. ;
Weiss, D. .
NEW JOURNAL OF PHYSICS, 2009, 11
[5]   Peculiar localized state at zigzag graphite edge [J].
Fujita, M ;
Wakabayashi, K ;
Nakada, K ;
Kusakabe, K .
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1996, 65 (07) :1920-1923
[6]   Electronic properties of graphene antidot lattices [J].
Furst, J. A. ;
Pedersen, J. G. ;
Flindt, C. ;
Mortensen, N. A. ;
Brandbyge, M. ;
Pedersen, T. G. ;
Jauho, A-P .
NEW JOURNAL OF PHYSICS, 2009, 11
[7]   Charge transport gap in graphene antidot lattices [J].
Giesbers, A. J. M. ;
Peters, E. C. ;
Burghard, M. ;
Kern, K. .
PHYSICAL REVIEW B, 2012, 86 (04)
[8]   Transport through graphene quantum dots [J].
Guettinger, J. ;
Molitor, F. ;
Stampfer, C. ;
Schnez, S. ;
Jacobsen, A. ;
Droescher, S. ;
Ihn, T. ;
Ensslin, K. .
REPORTS ON PROGRESS IN PHYSICS, 2012, 75 (12)
[9]   Energy band-gap engineering of graphene nanoribbons [J].
Han, Melinda Y. ;
Oezyilmaz, Barbaros ;
Zhang, Yuanbo ;
Kim, Philip .
PHYSICAL REVIEW LETTERS, 2007, 98 (20)
[10]   Controlled Formation of Sharp Zigzag and Armchair Edges in Graphitic Nanoribbons [J].
Jia, Xiaoting ;
Hofmann, Mario ;
Meunier, Vincent ;
Sumpter, Bobby G. ;
Campos-Delgado, Jessica ;
Romo-Herrera, Jose Manuel ;
Son, Hyungbin ;
Hsieh, Ya-Ping ;
Reina, Alfonso ;
Kong, Jing ;
Terrones, Mauricio ;
Dresselhaus, Mildred S. .
SCIENCE, 2009, 323 (5922) :1701-1705