Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested.

Electron-phonon interaction in atomic-scale conductors: Einstein oscillators versus full phonon modes

Two extreme pictures of electron-phonon interactions in nanoscale conductors are compared: one in which the vibrations are treated as independent Einstein atomic oscillators, and one in which electrons are allowed to couple to the full, extended phonon modes of the conductor. It is shown that, under a broad range of conditions, the full-mode picture and the Einstein picture produce essentially the same net power at any given atom in the nanojunction. The two pictures begin to differ significantly in the limit of low lattice temperature and low applied voltages, where electron-phonon scattering is controlled by the detailed phonon energy spectrum. As an illustration of the behaviour in this limit, we study the competition between trapped vibrational modes and extended modes in shaping the inelastic current-voltage characteristics of one-dimensional atomic wires.

Inelastic current-voltage spectroscopy of atomic wires

A tight-binding model is developed to describe the electron-phonon coupling in atomic wires under an applied voltage and to model, their inelastic current-voltage spectroscopy. Particular longitudinal phonons are found to have greatly enhanced coupling to the electronic states of the system. This leads to a large drop in differential conductance at threshold energies associated with these phonons. It is found that with increasing tension these energies decrease, while the size of the conductance drops increases, in agreement with experiment.

Power dissipation in nanoscale conductors

A previous tight-binding model of power dissipation in a nanoscale conductor under an applied bias is extended to take account of the local atomic topology and the local electronic structure. The method is used to calculate the power dissipated at every atom in model nanoconductor geometries: a nanoscale constriction, a one-dimensional atomic chain between two electrodes with a resonant double barrier, and an irregular nanowire with sharp corners. The local power is compared with the local current density and the local density of states. A simple relation is found between the local power and the current density in quasiballistic geometries. A large enhancement in the power at special atoms is found in cases of resonant and anti-resonant transmission. Such systems may be expected to be particularly unstable against current-induced modifications.

Predation on mayfly nymph, Baetis rhodani, by native and introduced Gammarus: direct effects and the facilitation of predation by salmonids.

1. In a series of laboratory experiments, we assessed the predatory nature of the native Irish amphipod, Gammarus duebeni celticus, and the introduced G. pulex, towards the mayfly nymph Baetis rhodani. We also investigated alterations in microhabitat use and drift behaviour of B. rhodani in the presence of Gammarus, and indirect predatory interactions with juvenile Atlantic salmon, Salmo salar. 2. In trials with single predators and prey, B. rhodani survival was significantly lower when Gammarus were free to interact with nymphs as than when Gammarus were isolated from them. The invader G. pulex reduced the survival of B. rhodani more rapidly than did the native G. d. celticus. Both Gammarus spp. were active predators. 3. In `patch' experiments, B. rhodani survival was significantly lower both when G. pulex and G. d. celticus were present, although the effect of the two Gammarus species did not differ. Again, active predation of nymphs by Gammarus was observed. Significantly more nymphs occurred on the top and sides of a tile, and per capita drifts were significantly higher, when Gammarus were present. Baetis rhodani per capita drift was also significantly higher in the presence of the introduced G. pulex than with the native G. d. celticus. 4. Gammarus facilitated predation by salmon parr of B. rhodani by significantly increasing fish–nymph encounters on exposed gravel and in the drift. There were no differential effects of the two Gammarus spp. on fish –B. rhodani encounters or consumption. 5. We conclude that Gammarus as a predator can have lethal, nonlethal, direct and indirect effects in freshwaters. We stress the need for recognition of this predatory role when assigning Gammarus spp. to a `Functional Feeding Group'.