Topological confinement in an antisymmetric potential in bilayer graphene in the presence of a magnetic field
© Zarenia et al; licensee Springer. 2011
Received: 16 September 2010
Accepted: 14 July 2011
Published: 14 July 2011
We investigate the effect of an external magnetic field on the carrier states that are localized at a potential kink and a kink-antikink in bilayer graphene. These chiral states are localized at the interface between two potential regions with opposite signs.
PACS numbers: 71.10.Pm, 73.21.-b, 81.05.Uw
Carbon-based electronic structures have been the focus of intense research since the discovery of fullerenes and carbon nanotubes. More recently, the production of atomic layers of hexagonal carbon (graphene) has renewed that interest, with the observation of striking mechanical and electronic properties, as well as ultrarelativistic-like phenomena in condensed matter systems[2–4]. In that context, bilayer graphene (BLG), which is a system with two coupled sheets of graphene, has been shown to have features that make it a possible substitute of silicon in microelectronic devices. The carrier dispersion of pristine BLG is gapless and approximately parabolic at two points in the Brillouin zone (K and K'). However, it has been found that the application of perpendicular electric fields produced by external gates deposited on the BLG surface can induce a gap in the spectrum. The electric field creates a charge imbalance between the layers which leads to a gap in the spectrum[5, 6]. The tailoring of the gap by an external field may be particularly useful for the development of devices. It has been recently recognized that a tunable energy gap in BLG can allow the observation of new confined electronic states[7, 8], which could be obtained by applying a spatially varying potential profile to create a position-dependent gap analogous to semiconductor heterojunctions.
An additional tool for the manipulation of charge states is the use of magnetic fields. The application of an external magnetic field perpendicular to the BLG sheet causes the appearance of Landau levels which can be significantly modified by the induced gap, leading to effect s such as the lifting of valley degeneracy caused by the breaking of the inversion symmetry due to the electrostatic bias[12, 13]. The presence of a magnetic field in conjunction with electrostatic potential barriers in BLG has been shown to lead to a rich set of behaviors in which Landau quantization competes with the electrostatic confinement-induced quantization.
In the present work we investigate the properties of localized states in a kink potential profile under a perpendicular external magnetic field, both for the case of a single potential kink, as well as for a kink-antikink pair. One advantage of such a setup is the fact that in an experimental realization of this system the number of one-dimensional metallic channels and their subsequent magnetic response can be configurable, by controlling the gate voltages. As shown by our numerical results, the influence of the magnetic field can be strikingly distinct for single and double kinks.
where, u b is the maximum value of the gate voltage in dimensionless unit in each BLG layer. Here, δ denotes the width of the region in which the potential switches its sign in each layer. This parameter is determined by the distance between the gates used to create the energy gap. We solved numerically Eqs. (3) using the finite element technique to obtain the the spectrum as function of the magnetic field and the potential parameters.
I. Numerical Results
We obtained the spectrum of electronic bound states that are localized at potential kinks in bilayer graphene, which can be created by antisymmetric gate potentials. For a single potential kink, the bound states are only weakly influenced by an external magnetic field, due to their one-dimensional character, caused by the strong confinement along the direction of the potential kink interface. For a kink-antikink pair, however, the numerical results show a significant shift of the carrier dispersion, which arises due to the coupling of the states localized at either potential interface. Therefore, such configurable kink potentials in bilayer graphene permits the tailoring of the low-dimensional carrier dynamics as well as its magnetic field response by means of gate voltages.
This work was supported by the Brazilian agency CNPq (Pronex), the Flemish Science Foundation (FWO-Vl), the Belgian Science Policy (IAP), and the bilateral projects between Flanders and Brazil and FWO-CNPq.
- Saito R, Dresslhaus G, Dresselhaus MS: Physical Properties of Carbon Nanotubes. Imperial College Press, London; 1998.
- Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim A: The electronic properties of grapheme. Rev Mod Phys 2009, 81: 109. 10.1103/RevModPhys.81.109View Article
- Li X, Wang X, Zhang Li, Lee S, Dai H: Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008, 319: 1229. 10.1126/science.1150878View Article
- Ohta T, Bostwick A, Seyller T, Horn K, Rotenberg E: Controlling the Electronic Structure of Bilayer Graphene. Science 2006, 313: 951. 10.1126/science.1130681View Article
- McCann E: Asymmetry gap in the electronic band structure of bilayer grapheme. Phys Rev B 2006, 74: 161403.View Article
- Castro EduardoV, Novoselov KS, Morozov SV, Peres NMR, Lopes dos Santos JMB, Nilsson Johan, Guinea F, Geim AK, Castro Neto AH: Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect. Phys Rev Lett 2007, 99: 216802.View Article
- Pereira JM Jr, Vasilopoulos P, Peeters FM: Tunable Quantum Dots in Bilayer Graphene. Nano Lett 2007, 7: 946. 10.1021/nl062967sView Article
- Zarenia M, Pereira JM Jr, Peeters FM, Farias GA: Electrostatically Confined Quantum Rings in Bilayer Graphene. Nano Lett 2009, 9: 4088. 10.1021/nl902302mView Article
- Martin I, Blanter YaM, Morpurgo AF: Topological Confinement in Bilayer Graphene. Phys Rev Lett 2008, 100: 036804.View Article
- Killi M, Wei T-C, Affleck I, Paramekanti A: Tunable Luttinger Liquid Physics in Biased Bilayer Graphene. Phys Rev Lett 2010, 104: 216406.View Article
- Jing L, Velasco J Jr, Kratz P, Liu G, Bao W, Bockrath M, Lau CN: Quantum Transport and Field-Induced Insulating States in Bilayer Graphene pnp Junctions. Nano Lett 2010, 10: 4775. 10.1021/nl103406bView Article
- McCann E, Fal'ko VI: Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer. Phys Rev Lett 2006, 96: 086805.View Article
- Pereira JM, Peeters FM, Vasilopoulos P: Landau levels and oscillator strength in a biased bilayer of grapheme. Phys Rev B 2007, 76: 115419.View Article
- Pereira JM, Peeters FM, Vasilopoulos P, Costa Filho RN, Farias GA: Landau levels in graphene bilayer quantum dots. Phys Rev B 79: 195403.
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.