T. Frederiksen, N. Lorente, M. Paulsson, and M. Brandbyge

**From tunneling to contact: Inelastic signals in an atomic gold junction from first principles**

Phys. Rev. B **75**, 235441 (2007) [cond-mat/0702176]

The evolution of electron conductance in the presence of inelastic effects is studied as an atomic gold contact is formed evolving from a low-conductance regime (tunneling) to a high-conductance regime (contact). In order to characterize each regime, we perform density-functional theory (DFT) calculations to study the geometric and electronic structures, together with the strength of the atomic bonds and the associated vibrational frequencies. The conductance is calculated by, first, evaluating the transmission of electrons through the system and, second, by calculating the conductance change due to the excitation of vibrations. As found in previous studies [Paulsson et al., Phys. Rev. B **72**, 201101(R) (2005)], the change in conductance due to inelastic effects permits us to characterize the crossover from tunneling to contact. The most notorious effect is the crossover from an increase in conductance in the tunneling regime to a decrease in conductance in the contact regime when the bias voltage matches a vibrational threshold. Our DFT-based calculations actually show that the effect of vibrational modes in electron conductance is rather complex, in particular, when modes localized in the contact region are permitted to extend into the electrodes. As an example, we find that certain modes can give rise to decreases in conductance when in the tunneling regime, opposite to the above-mentioned result. Whereas details in the inelastic spectrum depend on the size of the vibrational region, we show that the overall change in conductance is quantitatively well approximated by the simplest calculation where only the apex atoms are allowed to vibrate. Our study is completed by the application of a simplified model where the relevant parameters are obtained from the above DFT-based calculations.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho

**Inelastic transport theory from first principles: methodology and application to nanoscale devices**

Phys. Rev. B **75**, 205413 (2007) [cond-mat/0611562]

We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TRANSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green's function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born approximation. While these calculations often are computationally demanding, we show how they can be approximated by a simple and efficient lowest order expansion. Our method also addresses effects of energy dissipation and local heating of the junction via detailed calculations of the power flow. We demonstrate the developed procedures by considering inelastic transport through atomic gold wires of various lengths, thereby extending the results presented in Frederiksen et al. [Phys. Rev. Lett. **93**, 256601 (2004)]. To illustrate that the method applies more generally to molecular devices, we also calculate the inelastic current through different hydrocarbon molecules between gold electrodes. Both for the wires and the molecules our theory is in quantitative agreement with experiments, and characterizes the system-specific mode selectivity and local heating.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho

**
First-principles theory of inelastic transport and local heating in atomic gold wires**

AIP Conf. Proc. **893**, 727-728 (2007)

We present theoretical calculations of the inelastic transport properties in atomic gold wires. Our method is based on a combination of density functional theory and nonequilibrium Green's functions. The vibrational spectra for extensive series of wire geometries have been calculated using SIESTA, and the corresponding effects in the conductance are analyzed. In particular, we focus on the heating of the active vibrational modes. By a detailed comparison with experiments we are able to estimate an order of magnitude for the external damping of the active vibrations.

T. Frederiksen, M. Paulsson, and M. Brandbyge

**Inelastic Fingerprints of Hydrogen Contamination in Atomic Gold Wire Systems**

J. Phys.: Conf. Ser. **61**, 312-316 (2007) [cond-mat/0608510]

We present series of first-principles calculations for both pure and hydrogen contaminated gold wire systems in order to investigate how such impurities can be detected. We show how a single H atom or a single H_{2} molecule in an atomic gold wire will affect forces and Au-Au atom distances under elongation. We further determine the corresponding evolution of the low-bias conductance as well as the inelastic contributions from vibrations. Our results indicate that the conductance of gold wires is only slightly reduced from the conductance quantum G_{0} = 2e^{2}/h by the presence of a single hydrogen impurity, hence making it difficult to use the conductance itself to distinguish between various configurations. On the other hand, our calculations of the inelastic signals predict significant differences between pure and hydrogen contaminated wires, and, importantly, between atomic and molecular forms of the impurity. A detailed characterization of gold wires with a hydrogen impurity should therefore be possible from the strain dependence of the inelastic signals in the conductance.

N. Néel, J. Kröger, L. Limot, T. Frederiksen, M. Brandbyge, and R. Berndt

**Controlled Contact to a C _{60} Molecule**

Phys. Rev. Lett.

The tip of a low-temperature scanning tunneling microscope is approached towards a C_{60} molecule adsorbed at a pentagon-hexagon bond on Cu(100) to form a tip-molecule contact. The conductance rapidly increases to ~0.25 conductance quanta in the transition region from tunneling to contact. Ab-initio calculations within density functional theory and nonequilibrium Green's function techniques explain the experimental data in terms of the conductance of an essentially undeformed C_{60}. The conductance in the transition region is affected by structural fluctuations which modulate the tip-molecule distance.

T. Frederiksen,

**
Inelastic transport theory for nanoscale systems**

PhD thesis, MIC, DTU, February 2007.
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This thesis describes theoretical and numerical investigations of inelastic scattering and energy dissipation in electron transport through nanoscale systems. A computational scheme, based on a combination of density functional theory (DFT) and nonequilibrium Green's functions (NEGF), has been developed to describe the electrical conduction properties taking into account the full atomistic details of the systems. The scheme involves quantitative calculations of electronic structure, vibrational modes and frequencies, electron-vibration couplings, and inelastic current-voltage characteristics in the weak coupling limit.

When a current is passed through a nanoscale device, such as a single molecule or an atomic-size contact, it will heat up due to excitations of the nuclear vibrations. The developed scheme is able to quantify this local heating effect and to predict how it affects the conductance.

The methods have been applied to a number of specific systems, including monatomic gold chains, atomic point contacts, and metal-molecule-metal configurations. These studies have clarified the inelastic effects in the electron transport and characterized the vibrational modes that couple to the current. For instance, the dominant scattering for gold chains could be traced back to the longitudinal "alternating bond-length" mode. Furthermore, the results have been compared critically with experimental measurements for the different systems, and provided a microscopic understanding for the important physics. An example is the current-induced fluctuations that have been shown to influence the transport though individual C 60 molecules on copper surfaces.