Energy gap opening in submonolayer lithium on graphene: Local density functional and tight-binding calculations

M. Farjam and H. Rafii-Tabar

Phys. Rev. B 79, 045417 – Published 21 January 2009

Abstract

The adsorption of an alkali-metal submonolayer on graphene occupying every third hexagon of the honeycomb lattice in a commensurate $(\sqrt{3} \times \sqrt{3}) R 30 °$ arrangement induces an energy gap in the spectrum of graphene. To exemplify this type of band gap, we present ab initio density functional theory calculations of the electronic band structure of $C_{6} Li$ . An examination of the lattice geometry of the compound system shows the possibility that the nearest-neighbor hopping amplitudes have alternating values constructed in a Kekulé-type structure. The band structure of the textured tight-binding model is calculated and shown to reproduce the expected band gap as well as other characteristic degeneracy removals in the spectrum of graphene induced by lithium adsorption. More generally we also deduce the possibility of energy gap opening in periodic metal on graphene compounds $C_{x} M$ if $x$ is a multiple of 3.

Received 9 September 2008

DOI:https://doi.org/10.1103/PhysRevB.79.045417

Authors & Affiliations

M. Farjam¹ and H. Rafii-Tabar^1,2

¹Department of Nano-Science, Computational Physical Sciences Laboratory, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
²Department of Medical Physics and Biomedical Engineering and Research Centre for Medical Nanotechnology and Tissue Engineering, Shahid Beheshti University of Medical Sciences, Evin, Tehran 19839, Iran

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Vol. 79, Iss. 4 — 15 January 2009

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Images

Figure 1
(a) Band structure of $C_{6} *$ , i.e., graphene described by the unit cell of $(\sqrt{3} \times \sqrt{3}) R 30 °$ structure. (b) Band structure of $C_{6} Li$ . A band gap has opened at the neutrality point, the degenerate bands along the $Γ − K$ direction are split, and a small band gap has opened at $K$ near the bottom of the figure. Horizontal dashed lines indicate the Fermi levels of the respective systems.Reuse & Permissions
Figure 2
(Color online) Lattice structure of lithium on graphene $C_{6} Li$ . Carbon atoms on sublattices $A$ and $B$ are depicted as filled and open black circles. Lithium atoms, in magenta (very light gray), occupy positions above the hollow sites. The dashed hexagon is the Wigner-Seitz primitive unit cell of $C_{6} Li$ , containing six numbered C atoms and one Li atom. Two types of bonds, two-thirds red (light gray) and one-third blue (dark gray), are distinguished due to the presence of Li atoms. On the lower left, the rhombus defined by $c_{1}$ and $c_{2}$ and enclosing two carbon atoms is the primitive unit cell of graphene. The $30 °$ rotated rhombus, defined by $a_{1}$ and $a_{2}$ and having $\sqrt{3}$ times larger side, is the unit cell of $C_{6} Li$ . In the upper left part are shown the vectors pointing from a carbon atom on sublattice $A$ to its three nearest neighbors on sublattice $B$ . The inset shows the reciprocal space. The vectors $b_{1, 2}$ and $d_{1, 2}$ are sets of reciprocal-lattice vectors of $C_{6} Li$ and graphene, respectively. The hexagons in the inset are the Brillouin zones. The region defined by $Γ K M$ is the irreducible wedge of graphene Brillouin zone.Reuse & Permissions
Figure 3
Band structures of graphene in the Brillouin zones of (a) the $(1 \times 1)$ structure, and (b) the $(\sqrt{3} \times \sqrt{3}) R 30 °$ structure.Reuse & Permissions
Figure 4
Band structures of graphene from the TB model with two hopping amplitudes: (a) $t_{1} = 2.79 eV$ , $t_{2} = 2.59 eV$ , and (b) $t_{1} = 2.59 eV$ , $t_{2} = 2.79 eV$ . Note that the threefold degeneracies at $K$ , e.g., the lower left one, are lifted so that in (a) we have first a nondegenerate level and above it a doubly degenerate level, and in (b) we have just the opposite order of the degenerate and nondegenerate levels.Reuse & Permissions
Figure 5
(Color online) (a) DOS of $C_{6} Li$ calculated by DFT code. The vertical red line indicates the position of the Fermi level. (b) The corresponding DOS for graphene calculated within the tight-binding model. The position of Van Hove singularities are displaced relative to the DOS of (a) and the extra densities corresponding to Li atoms are not included in (b).Reuse & Permissions

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