Reverse Exponential Decay of Electrical Transmission in Nanosized Graphite Sheets

Abstract

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 ) g 0 e -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.

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation

“…In the anthracene and tetracene cases, G also increases with the number of units, whereas in naphthalene the conductance remains almost constant with the chain length. It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets . Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wave function instabilities appear.…”

“…It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets. 15 Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wavefunction instabilities appear. As stated, reversed exponential decay is found in systems where frontier orbitals are almost degenerate and distant energetically from the valence and conduction bands.…”

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation

“…In the anthracene and tetracene cases, G also increases with the number of units, whereas in naphthalene the conductance remains almost constant with the chain length. It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets . Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wave function instabilities appear.…”

“…It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets. 15 Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wavefunction instabilities appear. As stated, reversed exponential decay is found in systems where frontier orbitals are almost degenerate and distant energetically from the valence and conduction bands.…”

Length dependence of electron transport through molecular wires – a first principles perspective

“…In this review, we have focused on a first principles theory perspective of electron transport through molecular wires, applicable in the off-resonant tunneling regime. We show that 41 S 0.3 (tunnelling regime) 0.09 (hopping regime) 7-AGNR 162 No link group 0.45 AE 0.06 (low bias) B10 À2 0.1-0.2 (high bias) B10 À2 AGNR sheet 163 Zigzag edge atom (gold chain as leads) Hybrid-DFT: B0.117 Hybrid-DFT: B10 À3 AGNR 164 Zigzag edge (wider AGNR as leads) DFT: B0 DFT: 0-1 tunable with bias (8,0) CNT 103 DFT-CBS: B0.12 complex band structure calculations are helpful to provide a quick estimate of the decay constant beta, but they neglect effects of the metal-molecule geometry, which are significant and need to be considered for quantitative predictions of conductance and beta. The Landauer-Buttiker formalism, which explicitly takes into account contact geometries, is a useful tool to predict conductance, thermopower and beta values in molecular wires.…”

Diradical Character as a Guiding Principle for the Insightful Design of Molecular Nanowires with an Increasing Conductance with Length

“…Whereas the first genuine experimental observation of this nonclassical behavior still has to be realized (though both bias- and solvent-driven reverse exponential decay have been reported very recently), , a growing number of candidate wires have been proposed theoretically. The so-called “reverse-exponential decay” of molecular conductance was first reported by Yoshizawa and Tada for nanographenes; these results were later on corroborated by Li et al Mandado and his co-workers described a similar reverse exponential decay of the conductance in quinoid wires. , Later on, Tsuji and co-workers predicted that polyenes with reverse bond alternation patterns would also exhibit this nonclassical behavior . This realization has recently led to the proposal of cumulenes as interesting candidates for anti-Ohmic molecular wires (Figure ).…”

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation

“…In the anthracene and tetracene cases, G also increases with the number of units, whereas in naphthalene the conductance remains almost constant with the chain length. It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets . Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wave function instabilities appear.…”

“…It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets. 15 Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wavefunction instabilities appear. As stated, reversed exponential decay is found in systems where frontier orbitals are almost degenerate and distant energetically from the valence and conduction bands.…”

Length dependence of electron transport through molecular wires – a first principles perspective

“…In this review, we have focused on a first principles theory perspective of electron transport through molecular wires, applicable in the off-resonant tunneling regime. We show that 41 S 0.3 (tunnelling regime) 0.09 (hopping regime) 7-AGNR 162 No link group 0.45 AE 0.06 (low bias) B10 À2 0.1-0.2 (high bias) B10 À2 AGNR sheet 163 Zigzag edge atom (gold chain as leads) Hybrid-DFT: B0.117 Hybrid-DFT: B10 À3 AGNR 164 Zigzag edge (wider AGNR as leads) DFT: B0 DFT: 0-1 tunable with bias (8,0) CNT 103 DFT-CBS: B0.12 complex band structure calculations are helpful to provide a quick estimate of the decay constant beta, but they neglect effects of the metal-molecule geometry, which are significant and need to be considered for quantitative predictions of conductance and beta. The Landauer-Buttiker formalism, which explicitly takes into account contact geometries, is a useful tool to predict conductance, thermopower and beta values in molecular wires.…”

Diradical Character as a Guiding Principle for the Insightful Design of Molecular Nanowires with an Increasing Conductance with Length

“…Whereas the first genuine experimental observation of this nonclassical behavior still has to be realized (though both bias- and solvent-driven reverse exponential decay have been reported very recently), , a growing number of candidate wires have been proposed theoretically. The so-called “reverse-exponential decay” of molecular conductance was first reported by Yoshizawa and Tada for nanographenes; these results were later on corroborated by Li et al Mandado and his co-workers described a similar reverse exponential decay of the conductance in quinoid wires. , Later on, Tsuji and co-workers predicted that polyenes with reverse bond alternation patterns would also exhibit this nonclassical behavior . This realization has recently led to the proposal of cumulenes as interesting candidates for anti-Ohmic molecular wires (Figure ).…”

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation

“…In the anthracene and tetracene cases, G also increases with the number of units, whereas in naphthalene the conductance remains almost constant with the chain length. It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets . Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wave function instabilities appear.…”

“…It can be observed how the trends are similar to those observed by Tada et al in nanosized graphene sheets. 15 Unfortunately, and importantly, we remark that it is in those structures in which the conductance is larger where the above-mentioned wavefunction instabilities appear. As stated, reversed exponential decay is found in systems where frontier orbitals are almost degenerate and distant energetically from the valence and conduction bands.…”

Length dependence of electron transport through molecular wires – a first principles perspective

“…In this review, we have focused on a first principles theory perspective of electron transport through molecular wires, applicable in the off-resonant tunneling regime. We show that 41 S 0.3 (tunnelling regime) 0.09 (hopping regime) 7-AGNR 162 No link group 0.45 AE 0.06 (low bias) B10 À2 0.1-0.2 (high bias) B10 À2 AGNR sheet 163 Zigzag edge atom (gold chain as leads) Hybrid-DFT: B0.117 Hybrid-DFT: B10 À3 AGNR 164 Zigzag edge (wider AGNR as leads) DFT: B0 DFT: 0-1 tunable with bias (8,0) CNT 103 DFT-CBS: B0.12 complex band structure calculations are helpful to provide a quick estimate of the decay constant beta, but they neglect effects of the metal-molecule geometry, which are significant and need to be considered for quantitative predictions of conductance and beta. The Landauer-Buttiker formalism, which explicitly takes into account contact geometries, is a useful tool to predict conductance, thermopower and beta values in molecular wires.…”

Diradical Character as a Guiding Principle for the Insightful Design of Molecular Nanowires with an Increasing Conductance with Length

“…Whereas the first genuine experimental observation of this nonclassical behavior still has to be realized (though both bias- and solvent-driven reverse exponential decay have been reported very recently), , a growing number of candidate wires have been proposed theoretically. The so-called “reverse-exponential decay” of molecular conductance was first reported by Yoshizawa and Tada for nanographenes; these results were later on corroborated by Li et al Mandado and his co-workers described a similar reverse exponential decay of the conductance in quinoid wires. , Later on, Tsuji and co-workers predicted that polyenes with reverse bond alternation patterns would also exhibit this nonclassical behavior . This realization has recently led to the proposal of cumulenes as interesting candidates for anti-Ohmic molecular wires (Figure ).…”