8978
J. Phys. Chem. B 1998, 102, 8978-8980
Asymmetric I/V Characteristics in Nonalternant Carbon Networks Gabin Treboux,* Paul Lapstun, and Kia Silverbrook SilVerbrook Research, P.O. Box 207, Balmain 2041, NSW Australia ReceiVed: June 16, 1998; In Final Form: August 19, 1998
Carbon rings containing an odd number of atoms have a nonalternant character which causes an intrinsic charge separation. This is due to an asymmetry between electron and hole states in the local density of states. This feature is analyzed in detail for the case of the azulene molecule. We show that nonalternant character leads to an asymmetry in the I/V characteristic of such molecules, as well as to different electron and hole transport regimes.
Introduction Recent experimental results demonstrate the potential of carbon nanotubes as nanoelectronic components.1 The insertion of five- and seven-membered rings in an otherwise regular sixmembered ring structure occurs naturally,2 and it has been shown theoretically that this modifies the electronic properties of the carbon nanotubes.3-6 We discuss azulene, an aromatic hydrocarbon consisting of a five-membered ring fused to a seven-membered ring (see Figure 1). Azulene, with its odd-membered rings, is a typical nonalternant molecule. In alternant systems, the atoms can be divided into two distinct sets, no atom of one set being adjacent to an atom of the other.7,8 Calling these sets starred {*} and unstarred {0} respectively, the molecular wave functions ψll′ can be written as *
ψll′ )
∑i
reservoir spectral density defined through Newns chemisorption theory15 as
{
βk2 ∆K(E) ) γ 0,
0
Cliφi (
∑j
Cl′jφj
(1)
In nonalternant systems, this electron-hole symmetry is lost. We show that the nonalternant character of a molecule leads to asymmetry in its I/V curve as well as to different electron and hole transport regimes. Model We implement the algorithm recently proposed by Mujica et al.9-11 for solving the general problem of electronic conduction between two reservoirs of states via a molecular wire. In the approach of Mujica et al. the system consists of a molecule bridging two noninteracting reservoirs of states (see Figure 1). Using the T-matrix formalism of scattering theory,12-14 the quantum conductance is derived as
g)
Figure 1. Schematic representation of the azulene molecule connecting two reservoirs of states. The first atom of the molecule is connected to the left reservoir A and the last atom (N) to the right reservoir B. In the remainder of this article we define a forward voltage as a negative bias at A and a positive bias at B.
2e2 |G1N|2∆A(EF) ∆B(EF) πhh
(2)
where G is the Green’s function of the Hamiltonian of the total system, and EF is the Fermi energy. The subscript 1N stands for the matrix element connecting atoms 1 and N. ∆ is the * Corresponding author:
[email protected].
x1 - (2γE ) , 2
E | |
