Present trends in the miniaturization of electronic devices suggest that ultimately single molecules may be used as electronically active elements in a variety of applications. Recent advances in the manipulation of single molecules now permit to contact an individual molecule between two electrodes and measure its electronic transport properties. In contrast to single-electron transistors based on metallic islands, molecular devices have a more complicated, but in principle tunable, electronic structure. In addition to generic principles of nanoscale physics, e.g. Coulomb blockade, the chemistry and geometry of the molecular junction emerge as the fundamental tunable characteristics of molecular junctions.
In our group we have developed new theoretical tools to bridge traditional concepts of mesoscopic and molecular physics to describe transport through single molecules. In particular, in order to elucide the relation between the electronic structure of individual molecules and the conductance of the circuits in which they are embedded, we have combined ab initio quantum chemistry calculations, based on the density functional theory, with non-equilibrium Green functions techniques. This approach and constitutes a first step towards a quantitative theory for the a priori design of molecular devices.
We have used the approach mentioned above to describe transport through: single organic molecules [Reichert et al. PRL 88, 176804 (2002); J. Heurich et al., PRL 88, 256803 (2002)], a hydrogen molecule between Pt electrodes [Smit et al., Nature 419, 906 (2002); J.C. Cuevas et al., Nanotechnology 14, 29 (2003)], and atomic contacts [J.C. Cuevas et al., Nanotechnology 14, 29 (2003)].
Our current work is aimed at the understanding of the following issues in the electronic transport of single-molecule:
The appearance of experimental techniques such as the scanning tunneling microscope and breakjunctions has allowed to explore the electronic transport at the atomic scale [see N. Agrait et al., Phys. Rep. 377, 81 (2003)]. With these techniques it is possible to gently break a metallic contact and thus form conducting nanowires. During the last stages of the pulling a neck-shaped wire connects the two electrodes, the diameter of which is reduced to a single atom upon further stretching. The conductance of these contacts can be described by the Landauer formula: G=G0 ∑i Ti, where the sum runs over all the available conduction channels, Ti is the transmission for the i-th channel and G0=2e2/h is the quantum of conductance. It has been established that the channels in atomic contacts are determined by the valence orbitals of the central atoms, and the transmission of each channel is fixed by the atomic environment of the neck region [see E. Scheer et al., Nature 394, 154 (1998)].
In spite of the progress made in the last years in the understanding of the transport properties of these nanowires, there are still several basic open problems. In our group we have focused our theoretical efforts in resolving some of these puzzles. In particular, we have studied the following issues of special interest:
The nature of the conduction channels in metallic atomic wires has only been studied experimentally in four materials (Au, Al, Pb, and Nb) due to the need of superconductivity for the channel analysis [see E. Scheer et al., Nature 394, 154 (1998)]. In this sense, it was highly desirable to analyze other groups of metals. An interesting possibility is the analysis of the divalent metals of the IIB group of the periodic table such as Zn. In the collaboration with the experimental group of Elke Scheer (Universitaet Konstanz) we studied recently the nature of the conduction channels in one-atom Zn contacts. We have determined the transmission coefficients of atomic-sized Zn contacts using a new type of breakjunction which contains a whisker as a central bridge. We found that in the last conductance plateau the transport is unexpectedly dominated by a well-transmitting single conduction channel. We explained the experimental findings with the help of a tight-binding model which shows that in a one-atom Zn contact the current proceeds through the 4s and 4p orbitals of the central atom.
In the context of the transport properties of atomic-sized contacts there is a basic problem that still remains to be properly understood. Many experimental groups have investigated the conductance quantization in these nanowires. For this purpose, different groups have reported conductance histograms made of thousands different measurements of the breaking of these contacts. For some materials, noble metals and alkali metals, these histograms exhibit peaks close to integers of the quantum of conductance. Even in the cases in which there is clearly no sign of quantization, it is difficult to understand the origin of such peaks. Why are there preferred values of the conductance in these atomic wires?
In order to address this question we have established collaboration with the theoretical group of Prof. Peter Nielaba (Universitaet Konstanz). We have combined classical molecular dynamics simulations with conductance calculation based on a tight-binding model to analyze the influence of the mechanical properties in the conductance histograms of gold contacts. This combination gives us access to a great deal of information: geometry of the contacts, forces, minimum cross section, channel transmissions and total conductance. We have calculated conductance histograms for gold atomic contacts and we have shown that the peaks in the histograms are a result of a subtle interplay between the mechanical and electronic properties of gold. Moreover, we have studied the formation of chains of atoms and its signature in the conductance.
and conductance histogram of atomic-sized Au contacts
M. Dreher, F. Pauly, J. Heurich, J.C. Cuevas, E. Scheer, and P. Nielaba
Phys. Rev. B 72, 075435 (2005)
We have calculated the effect of electron-vibration coupling on conduction through atomic gold wires, which was measured in the experiments of Agrait et al. [Phys. Rev. Lett. 88, 216803 (2002)]. The vibrational modes, the coupling constants, and the inelastic transport are all calculated using a tight-binding parametrization and the non-equilibrium Green function formalism. The electron-vibration coupling gives rise to small drops in the conductance at voltages corresponding to energies of some of the vibrational modes. We study systematically how the position and height of these steps vary as a linear wire is stretched and more atoms are added to it, and find a good agreement with the experiments. In addition, we predict how the signatures of vibrational modes in the conductance curves differ between linear and zigzag-type wires.
interaction in transport through atomic gold wires
J.K. Viljas, J.C. Cuevas, F. Pauly, and M. Häfner
Phys. Rev. B 72, 245415 (2005)
Recently different experiments on the transport through atomic-sized contacts made of ferromagnetic materials have produced contradictory results. In particular, several groups have reported the observation of half-integer conductance quantization, which requires to have full spin polarization and perfectly conducting channels. Motivated by these surprising results, we have studied theoretically the conductance of atomic contacts of the ferromagnetic 3d materials Fe, Co and Ni using a realistic tight-binding model. Our analysis show that, at least in the absence of magnetic domains, the d bans of these transition metals play a very important role in the electrical conduction. This fact has the following important consequences for the three materials: (i) there are partially open conduction channels and therefore conductance quantization is not expected, (ii) the conductance of the last plateau is typically above G0=2e2/h, (iii) both spin bands contribute to the transport and thus there is no full spin polarization and (iv) both the value of the conductance and the current polarization are very sensitive to the contact geometry and disorder. Moreover, we have also combine our conductance calculations with realistic molecular dynamics simulations to investigate the conductance histogram of Ni contacts. Our results, in good agreement with the experiment of C. Untiedt et al. [Phys. Rev. B 69, 081401 (2004)], exhibits a first broad peak centered around 1.3G0.