T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho

**
Modeling of Inelastic Transport in One-dimensional Metallic Atomic Wires**

J. Comp. Electronics **3**, 423-427 (2004) [cond-mat/0411108]

Inelastic effects in electron transport through nano-sized devices are addressed with a method based on nonequilibrium Green's functions (NEGF) and perturbation theory to infinite order in the electron-vibration coupling. We discuss the numerical implementation which involves an iterative scheme to solve a set of coupled non-linear equations for the electronic Green's functions and the self-energies due to vibrations. To illustrate our method, we apply it to a one-dimensional single-orbital tight-binding description of the conducting electrons in atomic gold wires, and show that this simple model is able to capture most of the essential physics.

T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho

**
Inelastic Scattering and Local Heating in Atomic Gold Wires**

Phys. Rev. Lett. **93**, 256601 (2004) [cond-mat/0410700]

We present a method for including inelastic scattering in a first-principles density-functional computational scheme for molecular electronics. As an application, we study two geometries of four-atom gold wires corresponding to two different values of strain and present results for nonlinear differential conductance vs device bias. Our theory is in quantitative agreement with experimental results and explains the experimentally observed mode selectivity. We also identify the signatures of phonon heating.

M. C. Sullivan, T. Frederiksen, J. M. Repaci, D. R. Strachan, R. A. Ott, and C. J. Lobb

**Normal-Superconducting Phase Transition Mimicked by Current Noise**

Phys. Rev. B **70**, 140503(R) (2004) [cond-mat/0407144]

As a superconductor goes from the normal state into the superconducting state, the voltage versus current characteristics at low currents change from linear to nonlinear. We show theoretically and experimentally that the addition of current noise to nonlinear voltage versus current curves will create ohmic behavior. Ohmic response at low currents for temperatures below the critical temperature T_{c} mimics the phase transition and leads to incorrect values for T_{c} and the critical exponents ν and z. The ohmic response occurs at low currents, and will occur in both the zero-field transition and the vortex-glass transition. Our results indicate that the transition temperature and critical exponents extracted from the conventional scaling analysis are inaccurate if current noise is not filtered out. This is a possible explanation for the wide range of critical exponents found in the literature.

D. R. Strachan, M. C. Sullivan, T. Frederiksen, R. A. Ott, and C. J. Lobb

**What a superconducting transition should look like: extrapolating data from scaling plots**

Physica C **408-410**, 562-563 (2004)

We compare measured current-voltage measurements of a YBa_{2}Cu_{3}O_{7-δ} film with data extrapolated from various scaling collapses. We find that in general the extrapolated data show opposite concavity about the transition temperature at all currents; whereas the experimental data do not. This indicates that the experiments do not demonstrate unambiguous evidence for a superconducting transition.

M. C. Sullivan, D. R. Strachan, T. Frederiksen, R. A. Ott, M. Lilly, and C. J. Lobb

**Zero-Field Superconducting Phase Transition Obscured by Finite-Size Effects in Thick YBa _{2}Cu_{3}O_{7-δ} Films**

Phys. Rev. B

We report on the normal-superconducting phase transition in thick YBa_{2}Cu_{3}O_{7-δ} films in zero magnetic field. We find significant finite-size effects at low currents even in our thickest films (d=3200 Å). Using data at higher currents, we can unambiguously find T_{c} and z, and show z=2.1±0.15, as expected for the three-dimensional XY model with diffusive dynamics. The crossover to two-dimensional behavior, seen by other researchers in thinner films (d ≤ 500 Å), obscures the three-dimensional transition in both zero field and the vortex-glass transition in field, leading to incorrect values of T_{c} (or T_{g}), ν, and z. The finite-size effects, usually ignored in thick films, are an explanation for the wide range of critical exponents found in the literature.

T. Frederiksen,

**
Inelastic Electron Transport in Nanosystems**

MSc thesis, MIC, DTU, February 2004.
[ PDF ]

The emerging field of molecular electronics, in which individual molecules play the role of active devices, is receiving much attention due to its possible technological impact. Recent advances in nanoscale fabrication and engineering techniques have made it possible to study the transport properties of devices on the atomic scale. At this level one inherently probes the quantum mechanical nature of matter which manifests a number of effects not well understood yet. One such effect is the mutual interaction between electrical current and atomic vibrations.

In this thesis we describe a method for calculating dc current-voltage characteristics of nanostructures connected between metallic leads taking into account electron-vibration scattering inside the device. The method is based on nonequilibrium Green's functions (NEGF) and a Meir-Wingreen type formula for the current through an interacting region of space. Within the Born-Oppenheimer approximation we calculate the electronic Green's functions for this region treating the electron-phonon interaction perturbatively in the self-consistent Born approximation. The numerical implementation of the present method is discussed in detail, and we compare it with results in the literature as well as with our own calculations based on an exact diagonalization technique.

In particular we look at transport through metallic wires of single atoms. With a simple single-orbital tight-binding model and parameters fitted for Au chains we show how to determine the normal modes of vibration, the electron-vibration couplings, and the influence of the different modes on the conductance. Finally, we discuss the potential of combining our method with ab initio calculations of electronic structure, vibrational modes, and couplings, and present some preliminary results in this direction.