J. Phys. Chem. B 2004, 108, 7565-7572
7565
Reverse Exponential Decay of Electrical Transmission in Nanosized Graphite Sheets Tomofumi Tada and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering, Kyushu UniVersity, Fukuoka 812-8581, Japan ReceiVed: September 23, 2003; In Final Form: April 7, 2004
Quantum transport effects in a molecular junction composed of a nanosized graphite sheet and two gold leads are studied on the basis of Landauer’s formalism. The formulation for tunneling current by Caroli, Combescot, Nozieres, and Saint-James is extended to incorporate multiple interactions in a metal-insulator connecting region. A large variation of conductance is obtained, depending on the manner of connections between a graphite sheet and two gold chains. Connections between zigzag-edge sites and gold chains have significant transport effects. Graphite sheets of several sizes are studied to increase our understanding of the exponential law of conductance g ) g0e-γL, in which L is the molecular length and γ is the damping factor. Reverse exponential law with negative γ is observed in graphite sheets with zigzag edges. That is, the conductance is enhanced with an increase in L. This interesting behavior of conductance is due to the unique nature of the HOMO and LUMO localized in the zigzag-edge regions and the remarkable decrease in the HOMO-LUMO gap with L. Quantum transport effects in graphite sheets with defects such as a disordered zigzag edge are also studied. It is found that the regular zigzag-edge structures lead to effective quantum transport in graphite sheets.
Introduction
CHART 1
Electrical transmission through molecular junctions consisting of single molecules is an important issue in the development of molecular electronics in nanotechnology. Landauer’s formalism1,2 using a Green’s function method is of great use in calculating the conductance of molecular wires at the single molecule level, e.g., benzen-1,4-dithiol,3-8 fullerene C60,9-11 and tape-porphyrin oligomers.12 Sophisticated algorithms based on the formalism combined with density functional theory (DFT)13,14 were recently proposed.15-17 In the fundamental understanding of electrical transmission in molecular wires, issues of adsorption of molecules on electrodes, heteroatomic effects, and correlation between molecular length L and conductance are important. The exponential law of conductance g ) g0e-γL is useful to characterize molecular wires. Magoga and Joachim calculated the damping factor γ in several conjugated oligomers;18 for example, γ’s of the poly(acetylene) and poly(para-phenylene) oligomers shown in Chart 1 are 0.187 and 0.281 Å-1, respectively. The conductance therefore decreases with an increase in L. They also showed that good contact conductance g0 is obtained by optimizing the molecular wire end. Quantum transport effects in nanosized systems correlate with the electronic states of molecules incorporated into molecular junctions. In a previous paper, we derived an interesting relationship between frontier molecular orbitals (MOs) and conductance within Landauer’s formalism.19 We also studied heteroatomic effects on the conductance of nanosized graphite sheets.20 Since heteroatoms can localize the electronic population in the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO), quantum transport is significantly enhanced by heteroatoms. In the present paper, we derive a formulation for conductance by extending the one-dimensional model developed by Caroli, Combescot, Nozieres, and Saint-James (CCNS)21 and * To whom correspondence should be addressed. E-mail: kazunari@ ms.ifoc.kyushu-u.ac.jp.
present quantum transport effects in a molecular junction composed of a nanosized graphite sheet and two gold chains (chain-molecule-chain junction), in which we used a linear gold chain as a metallic lead. We used the B3LYP22 DFT method and the Pariser-Parr-Pople (PPP) method23 in this study. The molecular junctions adopted in this study are not unrealistic because multi-shell gold nanowires24 and onedimensional gold chains25 are available at present. We pay special attention to the exponential law of conductance and influences caused by defects in graphite sheets. Method of Calculation Extended CCNS Formulation. The formulation for tunneling current by CCNS21 provides a practical procedure for calculating electrical conductance on the basis of Landauer’s formalism. The system used in the CCNS formulation is a linear metal-insulator-metal (MIM) junction, in which the perturbation leading to electrical transmission is represented by a single interaction between M and I. To take multiple interactions into account, we extended the CCNS formulation to a general one. Figure 1a shows a schematic representation of a molecular junction composed of two linear gold chains and a molecule.
10.1021/jp0310908 CCC: $27.50 © 2004 American Chemical Society Published on Web 05/18/2004
7566 J. Phys. Chem. B, Vol. 108, No. 23, 2004
Tada and Yoshizawa and
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