Janne K. Viljas

Electron-phonon heat transfer in monolayer and bilayer graphene

We calculate the heat transfer between electrons to acoustic and optical phonons in monolayer and bilayer graphene (MLG and BLG) within the quasiequilibrium approximation. For acoustic phonons, we show how the temperature-power laws of the electron-phonon heat current for BLG differ from those previously derived for MLG and note that the high-temperature (neutral-regime) power laws for MLG and BLG are also different, with a weaker dependence on the electronic temperature in the latter. In the general case we evaluate the heat current numerically. We suggest that a measurement of the heat current could be used for an experimental determination of the electron-acoustic-phonon coupling constants, which are not accurately known. However, in a typical experiment heat dissipation by electrons at very low temperatures is dominated by diffusion and we estimate the crossover temperature at which acoustic-phonon coupling takes over in a sample with Joule heating. At even higher temperatures optical phonons begin to dominate. We study some examples of potentially relevant types of optical modes, including, in particular, the intrinsic in-plane modes and additionally the remote surface phonons of a possible dielectric substrate.

Density-functional study of tilt-angle and temperature-dependent conductance in biphenyl dithiol single-molecule junctions

Using a density-functional-based transport method we study the conduction properties of several biphenyl-derived dithiol (BPDDT) molecules wired to gold electrodes. The BPDDT molecules differ in their side groups, which control the degree of conjugation of the pi-electron system. We have analyzed the dependence of the low-bias zero-temperature conductance on the tilt angle phi between the two phenyl ring units, and find that it follows closely a cos^2(phi) law, as expected from an effective pi-orbital coupling model. We show that the tilting of the phenyl rings results in a decrease of the zero-temperature conductance by roughly two orders of magnitude, when going from a planar conformation to a configuration in which the rings are perpendicular. In addition we demonstrate that the side groups, apart from determining phi, have no influence on the conductance. All this is in agreement with the recent experiment by Venkataraman et al. [Nature 442, 904 (2006)]. Finally, we study the temperature dependence of both the conductance and its fluctuations and find qualitative differences between the examined molecules. In this analysis we consider two contributions to the temperature behavior, one coming from the Fermi functions and the other one from a thermal average over different contact configurations. We illustrate that the fluctuations of the conductance due to temperature-induced changes in the geometric structure of the molecule can be reduced by an appropriate design.

Electron-vibration interaction in transport through atomic gold wires

We calculate 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 nonequilibrium Green’s 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 good agreement with the experiments. We also consider two different types of geometries, which are found to yield qualitatively similar results. In contrast to previous calculations, we find that typically there are several close-lying drops due to different longitudinal modes. In the experiments, only a single drop is usually visible, but its width is too large to be accounted for by temperature. Therefore, to explain the experimental results, we find it necessary to introduce a finite broadening to the vibrational modes, which makes the separate drops merge into a single, wide one. In addition, we predict how the signatures of vibrational modes in the conductance curves differ between linear and zigzag-type wires.

Length-dependent conductance and thermopower in single-molecule junctions of dithiolated oligophenylene derivatives: A density functional study

We study theoretically the length dependence of both conductance and thermopower in metal-moleculemetal junctions made up of dithiolated oligophenylenes contacted to gold electrodes. We find that while the conductance decays exponentially with increasing molecular length, the thermopower increases linearly as suggested by recent experiments. We also analyze how these transport properties can be tuned with methyl side groups. Our results can be explained by considering the level shifts due to their electron-donating character as well as the tilt-angle dependence of conductance and thermopower. Qualitative features of the substituent effects in our density functional calculations are explained using a tight-binding model. In addition, we observe symmetry-related even-odd transmission channel degeneracies as a function of molecular length.

Conduction mechanisms in biphenyl dithiol single-molecule junctions

Based on density-functional theory calculations, we report a detailed study of the single-molecule charge-transport properties for a series of recently synthesized biphenyl-dithiol molecules. The torsion angle ϕ between the two phenyl rings, and hence the degree of π conjugation, is controlled by alkyl chains and methyl side groups. We consider three different coordination geometries, namely, top-top, bridge-bridge, and hollow-hollow, with the terminal sulfur atoms bound to one, two, and three gold surface atoms, respectively. Our calculations show that different coordination geometries give rise to conductances that vary by one order of magnitude for the same molecule. Irrespective of the coordination geometries, the charge transport calculations predict a cos2ϕ dependence of the conductance, which is confirmed by our experimental measurements. We demonstrate that the calculated transmission through biphenyl dithiols is typically dominated by a single transmission eigenchannel formed from π electrons. For perpendicular orientation of the rings a residual conductance arises from σ-π couplings. But only for a single molecule with a completely broken conjugation we find a nearly perfect degeneracy of the σ-π eigenchannels for the hollow-hollow-type contact in our theory.

Theoretical analysis of the conductance histograms and structural properties of Ag, Pt, and Ni nanocontacts

Conductance histograms are a valuable tool to study the intrinsic conduction properties of metallic atomicsized contacts. These histograms show a peak structure, which is characteristic of the type of metal under investigation. Despite the enormous progress in the understanding of the electronic transport in metallic nanowires, the origin of this peak structure is still a basic open problem. In the present work we tackle this issue, extending our theoretical analysis of Au conductance histograms Dreher et al., Phys. Rev. B 72, 075435 2005 to different types of metals, namely, Ag, Pt and ferromagnetic Ni. We combine classical molecular dynamics simulations of the breaking of nanocontacts with conductance calculations based on a tight-binding model. This combination gives us access to crucial information such as contact geometries, strain forces, minimum cross-sections, the conductance, transmissions of the individual conduction channels, and, in the case of Ni, the spin polarization of the current. We shall also briefly discuss investigations of Al atomic-sized contacts. From our analysis we conclude that the differences in the histograms of these metals are due to i the very different electronic structures, which means different atomic orbitals contributing to the transport and ii the different mechanical properties, which in a case such as Pt lead to the formation of special structures, namely, monoatomic chains. Of particular interest are results for Ni that indicate the absence of any conductance quantization, and show how the current polarization evolves including large fluctuations from negative values in thick contacts to even positive values in the tunneling regime after rupture of the contact. Finally, we also present a detailed analysis of the breaking forces of these metallic contacts, which are compared to the forces predicted from bulk considerations.

Modeling elastic and photoassisted transport in organic molecular wires : length dependence and current-voltage characteristics

Using a -orbital tight-binding model, we study the elastic and photoassisted transport properties of metalmolecule-metal junctions based on oligophenylenes of varying lengths. The effect of monochromatic light is modeled with an ac voltage over the contact. We first show how the low-bias transmission function can be obtained analytically, using methods previously employed for simpler chain models. In particular, the decay coefficient of the off-resonant transmission is extracted by considering both a finite-length chain and infinitely extended polyphenylene. Based on these analytical results, we discuss the length dependence of the linearresponse conductance, the thermopower, and the light-induced enhancement of the conductance in the limit of weak intensity and low frequency. In general, the conductance enhancement is calculated numerically as a function of the light frequency. Finally, we compute the current-voltage characteristics at finite dc voltages and show that in the low-voltage regime, the effect of low-frequency light is to induce current steps with a voltage separation determined by twice the frequency. These effects are more pronounced for longer molecules. We study two different profiles for the dc and ac voltages, and it is found that the results are robust with respect to such variations. Although we concentrate here on the specific model of oligophenylenes, the results should be qualitatively similar for many other organic molecules with a large enough electronic gap.

Proximity effect and multiple Andreev reflections in diffusive superconductor-normal-metal-superconductor junctions

We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function.

Ab initio study of the thermopower of biphenyl-based single-molecule junctions

By employing ab initio electronic-structure calculations combined with the nonequilibrium Green’s function technique, we study the dependence of the thermopower Q on the conformation in biphenyl-based single-molecule junctions. For the series of experimentally available biphenyl molecules, alkyl side chains allow us to gradually adjust the torsion angle ϕ between the two phenyl rings from 0 ◦ to 90 ◦ and to control in this way the degree of π -electron conjugation. Studying different anchoring groups and binding positions, our theory predicts that the absolute values of the thermopower decrease slightly towards larger torsion angles, following an a + b cos 2 ϕ dependence. The anchoring group determines the sign of Q and a,b simultaneously. Sulfur and amine groups give rise to Q,a,b > 0, while for cyano, Q,a,b < 0. The different binding positions can lead to substantial variations of the thermopower mostly due to changes in the alignment of the frontier molecular orbital levels and the Fermi energy. We explain our ab initio results in terms of a π -orbital tight-binding model and a minimal two-level model, which describes the pair of hybridizing frontier orbital states on the two phenyl rings. The variations of the thermopower with ϕ seem to be within experimental resolution.

Molecular dynamics study of the thermopower of Ag, Au, and Pt nanocontacts

Using molecular dynamics simulations of many junction stretching processes combined with tight-bindingbased electronic structure and transport calculations, we analyze the thermopower of silver (Ag), gold (Au), and platinum (Pt) atomic contacts. In all cases we observe that the thermopower vanishes on average within the standard deviation and that its fluctuations increase for a decreasing minimum cross section of the junctions. However, we find a suppression of the fluctuations of the thermopower for the s-valent metals Ag and Au, when the conductance originates from a single, perfectly transmitting channel. Essential features of the experimental results for Au, Ag, and copper (Cu) of Ludoph and van Ruitenbeek [Phys. Rev. B 59, 12290 (1999)], as yet unaddressed by atomistic studies, can hence be explained by considering the atomic and electronic structure at the disordered narrowest constriction of the contacts. For the multivalent metal Pt our calculations predict the fluctuations of the thermopower to be larger by one order of magnitude as compared to Ag and Au, and suppressions of the fluctuations as a function of the conductance are absent. Main features of our results are explained in terms of an extended single-level model.