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- Electronic transport through molecules

Start date: | 01.01.2000 |

End date: | 31.12.2004 |

Funded by: | Universität Augsburg |

Local head of project: | Gert-Ludwig Ingold |

External scientists / cooperations: |
Hermann Grabert (Freiburg) Abraham Nitzan (Tel Aviv) |

Publications: | Publication list |

With the increasing miniaturisation of electronic circuits, the use of molecular structures as building blocks in such circuits has recently received increasing attention. An important first goal is to understand the electronic transport through a molecule placed between two electrodes. While, in general, real molecules require extensive quantum chemistry calculations, this project aims at revealing fundamental physical processes in the electron transport through molecules by means of simple model systems. This includes studies of the incoherent transport through molecules, of the potential profile across a molecule as well as of the charge transport under the influence of a high-frequency field.

*Incoherent transport through molecular wires in the presence of strong Coulomb interaction*

The charge transport through a molecule placed between two electrodes can be coherent or incoherent, depending on the decoherence strength. Here, we consider incoherent transport described by hopping rates between adjacent building blocks of the molecule within a master equation approach. The Coulomb interaction is assumed to be so strong that not more than one additional electron can be present on the molecule. This leads to a blockade of electron transport as a function of the average excess charge on the molecular wire. In `LIH02` this blockade was studied in detail. Neglecting the electron spin in a first step, one finds that the current for different potential profiles along the wire depends differently on the number *N* of building blocks accounted for in the master equation. If the potential drops completely at the contacts between molecule and electrodes, the current decays like 1/*N*^{2} while for a linear potential profile it decays like 1/*N*. This difference thus offers a possibility to obtain information about the potential profile. If the electron spin is taken into account, the blockade depends on the ratio of the tunneling rates at the two contacts. If the tunneling rate at the right contact is much smaller than at the left contact, a current flowing from left to right will be strongly suppressed. In `LIH02` the temperature dependence of the blockade has been studied as well and it was shown that its form depends on the strength of the Coulomb interaction.

*Potential profile of molecular wires*

As just described, the form of the decay of the voltage between the contacts plays an important role for the current through the molecule. Again model systems have been employed in order to identify relevant properties of the potential profile without taking all details of the molecular structure into account. In `NGIG02` a Thomas-Fermi model for the screening was used in connection with the Poisson equation in order to determine the potential profile. Two parameters are of relevance for the potential profile: the screening length and the transversal extension of the molecule relative to its length. It turns out that with increasing thickness of the molecule a transition occurs from a linear potential profile to a profile in which the voltage mostly drops at the contacts while remaining nearly constant across the molecule. Conversely, a large screening length leads to a linear potential profile. Furthermore, it was shown that the potential profile for a chain of six gold atoms obtained by Damle et al. by means of *ab initio* methods can be well described by our model with an appropriate choice of model parameters.

This classical calculation is unable to describe quantum effects like Friedel oscillations of the electron density. Therefore, in `PGIN03` we have also carried out quantum calculations in Hartree-Fock approximation as well as with exact diagonalization. The molecule is modelled by a finite one-dimensional atom chain where the presence of the contacts is accounted for by the method of image charges. It turns out that the three-dimensional aspect of electrostatics is crucial for obtaining the correct potential profile. Now, a good agreement with the *ab initio* results for a chain of gold atoms could be obtained even without explicit fit and even the oscillations in the potential profile could be reproduced.

*Charge transport under the influence of a high-frequency field*

Exposing the molecule to an electromagnetic ac-field can lead to complex structures for current and noise properties like the Fano factor as a function of the field amplitude. In order to better understand these structures, in `KCSLIH04` the special case of a high-frequency field was studied. In this case a mapping onto a static model with effective parameters is possible.

We studied a model molecule consisting of two lattice sites placed between two electrodes. Electrons can hop, both, through contacts onto the molecule and between the two lattice sites. A high-frequency electromagnetic field periodically shifts the energies of the lattice sites with respect to each other. After the mapping onto an effective static model, the observed structures, e.g. in the Fano factor, can be explained in terms of three different scenarios. The largest Fano factor is obtained if the barrier between the two lattice sites dominates. If the two effective barriers at the contacts between the electrodes and the model molecule are more important, one finds a reduction of the Fano factor by one half as expected for a two-barrier system. Finally, the minimal Fano factor is obtained if effectively no relevant barriers are present. Through an appropriate choice of parameters, the noise properties of molecular transport can thus be tuned.

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