Quantum Inelastic Conductance through Molecular Wires

Abstract

We calculate nonperturbatively the inelastic effects on the conductance through a conjugated molecular-wire -metal heterojunction, including realistic electron-phonon coupling. We show that at subband-gap energies the current is dominated by quantum coherent transport of virtual polarons through the molecule. In this regime, the tunneling current is strongly increased relative to the case of elastic scattering. It is essential to describe the full quantum coherence of the polaron formation and transport in order to obtain correct physics. Our results are generally applicable to one-dimensional atomic or molecular wires. PACS numbers: 85.30.Vw, 73.40.Gk, 73.61.Ph Truly one-dimensional conducting structures, where the confinement lengths for electrons in two directions are of the order of atomic diameters, are currently the subject of much experimental work. Examples include fullerene nanotubes [1], organic molecules bonded to metallic electrodes [2], and dangling-bond (DB) wires created by scanning tunneling microscope lithography of the H-saturated Si(001) surface [3,4]. The conductance properties of such structures are of great importance when one considers their potential as atomic or molecular scale electronic devices. There have been many recent theoretical investigations of electron transport in these systems: for example, Joachim et al. studied Xe atom "wires" [5] and organic molecules [6] using the "elastic scattering quantum chemistry" approach; idealized one-dimensional atomic wires sandwiched between jellium electrodes have been studied using density functional theory [7] and a recursion transfer matrix method [8], while Datta and collaborators studied organic molecules on metal electrodes [9].All the above theoretical work was done within the approximation of elastic transport, where the electronphonon (e-ph) coupling plays no role. But there are good reasons to doubt the validity of this approximation in one-dimensional atomic or molecular scale systems. In small systems, the coupling between electron and other excitations is enhanced. Furthermore, a one-dimensional metal is generally unstable towards a Peierls distortion [10]. Once such a distortion has occurred and produced a band gap, charges added into the system tend to selflocalize and cause distortions of the system which lower the band gap. Such polaronic phenomena have been studied in conducting polymers for decades [11]; electron transport usually proceeds via tunneling into polaron states arising from lattice fluctuations [12].Motivated by this physics and the possibility of measuring the transport through one-dimensional atomic and molecular wires, we report in this Letter the first calculations of the inelastic electronic transport through an atomic-scale wire including realistic e-ph coupling. In our calculations, the quantum coherence of the states is fully retained, i.e., no adiabatic separation between the electronic and phonon degrees of freedom is made. We have chosen to study a conjugated molecular chain as an example since the...

Photon-phonon-assisted tunneling through a single-molecule quantum dot

“…Later on, this method has been further applied to the topic of inelastic electron scattering in mesoscopic quantum transport in semiconductor QDs and molecular wires under the framework of the Landauer-Büttiker scattering theory. 17,18 In this paper, we will redirect this procedure in terms of the NGF technique and address the inelastic PAT in a molecular QD.…”

Understanding electron flow in conducting polymer films: injection, mobility, recombination and mesostructure

“…This is because the injected electron (even for charge injection below the gap) induces distortions in the molecular lattice. We have already identified such distortions as being associated with the formation of a virtual polaron in the case of transport through the molecular wire (Ness et al (2001), Ness and Fisher (1999); see also next section). The polaron formation is also associated with a relaxation energy of the system.…”

“…when the electron and the atomic vibrations with which it interacts participate in a single, coherent, quantum-mechanical process. This is only true for relatively small individual parts of the transport process; in this paper, we apply this model primarily to the injection of charge into a molecule, but in our previous work (Ness and Fisher 1999, 2002a, 2002b, Ness et al 2001 we also considered a transport process that was entirely coherent throughout a single molecule. Such a coherent process corresponds to an idealized 'molecular electronics' experiment, rather than to transport in a real conducting polymer film.…”

Exploring the limits of the self-consistent Born approximation for inelastic electronic transport

“…Firstly, they play a role in transport 9,10 by opening new conductance channels through which the itinerant electrons can propagate, and by suppressing the transmission of purely elastic channels 11 . More dramatically, for large electron-phonon coupling the charge carriers become quasi-particles consisting of coupled electrons and phonons 12 . Secondly, from a technological point of view, phonons limit the efficiency of molecular devices because of energy dissipation.…”

“…Therefore one usually relies on atomistic simulation techniques in order to understand the results. For elastic transport, when electron-phonon interaction is not considered and the electron-electron interaction is treated at the mean field level, methods of note for predicting the current flowing through devices include the non-equilibrium Green function formalism (NEGF) 13,14,15,16,17 and scattering theory (ST) 12,18,19,20 . Some of these methods have been adapted to include electron-phonon interaction, notably an extension of scattering theory (EST) 11,21,22,23 and the self consistent Born approximation (SCBA) 24,25 within the NEGF formalism.…”