Title: Beyond Ehrenfest: correlated non-adiabatic molecular dynamics
Author(s): Horsfield A.P., Bowler D.R., Fisher A.J., Todorov T.N., Sanchez C.G.
Journal Of Physics-Condensed Matter, 16, No. 46, pp. 8251-8266 (NOV 24 2004)
A method for introducing correlations between electrons and ions that is computationally affordable is described. The central assumption is that the ionic wavefunctions are narrow, which makes possible a moment expansion for the full density matrix. To make the problem tractable we reduce the remaining many-electron problem to a single-electron problem by performing a trace over all electronic degrees of freedom except one. This introduces both one- and two-electron quantities into the equations of motion. Quantities depending on more than one electron are removed by making a Hartree-Fock approximation. Using the first-moment approximation, we perform a number of tight binding simulations of the effect of an electric current on a mobile atom. The classical contribution to the ionic kinetic energy exhibits cooling and is independent of the bias. The quantum contribution exhibits strong heating, with the heating rate proportional to the bias. However, increased scattering of electrons with increasing ionic kinetic energy is not observed. This effect requires the introduction of the second moment.
Title: Transport in nanoscale systems: the microcanonical versus grand-canonical picture
Author(s): Di Ventra M., Todorov T.N.
Journal Of Physics-Condensed Matter, 16, No. 45, pp. 8025-8034 (NOV 17 2004)
We analyse a picture of transport in which two large but finite charged electrodes discharge across a nanoscale junction. We identify a functional whose minimization, within the space of all bound many-body wavefunctions, defines an instantaneous steady state. We also discuss factors that favour the onset of steady-state conduction in such systems, make a connection with the notion of entropy, and suggest a novel source of steady-state noise. Finally, we prove that the true many-body total current in this closed system is given exactly by the one-electron total current, obtained from time-dependent density-functional theory.
Title: A Maxwell relation for current-induced forces
Author(s): Sutton A.P., Todorov T.N.
Molecular Physics, 102, No. 9-10, pp. 919-925 (MAY 10 2004)
A Maxwell relation is presented involving current-induced forces. It provides a new physical picture of the origin of current-induced forces and in the small-voltage limit it enables the identification of a simple thermodynamic potential which drives electromigration. The question of whether current-induced forces are conservative or non-conservative is discussed briefly in the light of these insights.
Title: Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
Author(s): Horsfield A.P., Bowler D.R., Fisher A.J., Todorov T.N., Montgomery M.J.
Journal Of Physics-Condensed Matter, 16, No. 21, pp. 3609-3622 (JUN 2 2004)
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.
Title: Are current-induced forces conservative?
Author(s): Di Ventra M., Chen Y.C., Todorov T.N.
Physical Review Letters, 92, No. 17, Art. No. 176803 (APR 30 2004)
The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential. On the other hand, there exist specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.