An ignition key for atomic-scale engines

Abstract

Abstract.A current-carrying resonant nanoscale device, simulated by non-adiabatic molecular dynamics, exhibits sharp activation of non-conservative current-induced forces with bias. The result, above the critical bias, is generalized rotational atomic motion with a large gain in kinetic energy. The activation exploits sharp features in the electronic structure, and constitutes, in effect, an ignition key for atomic-scale motors. A controlling factor for the effect is the non-equilibrium dynamical response matrix for small-amplitude atomic motion under current. This matrix can be found from the steady-state electronic structure by a simpler static calculation, providing a way to detect the likely appearance, or otherwise, of non-conservative dynamics, in advance of real-time modelling.Nanoscale conductors [1, 2] carry current densities orders of magnitude larger than in macroscopic wires, resulting in substantial forces. The current-induced force on a nucleus consists of (I) the average force, and (II) force noise originating from the corpuscular nature of electrons [3,4]. II causes inelastic electron-phonon scattering and Joule heating [2,5]. I contains the so-called electron-wind force, and velocity-dependent forces [3,4,[6][7][8][9][10][11]. The wind force results from momentum transfer in elastic electron-nuclear scattering, and drives electromigration [12]. Wind forces can be calculated from first principles, to study their effect on nanoscale devices [13][14][15][16].The electron-wind force is receiving fresh attention due to a remarkable property: it is non-conservative (NC) and can do net work on atoms around closed paths [3,4,[6][7][8][9][10][11][12]. This phenomenon, which we call the waterwheel effect, opens up interesting questions. It provides a mechanism for driving molecular engines [17][18][19][20][21][22]. But the gain in kinetic energy of the atoms from the work done by NC forces is also a potential failure mechanism, possibly more potent than Joule heating. There are experimental indications of anomalous biasactivated apparent heating in point contacts [23,24], above that expected from Joule heating alone [13,[25][26][27]. The waterwheel effect is a possible activation mechanism also for the electromigration phenomena that become a central issue under large currents [28,29].The applied bias is a key factor for the operation of NC forces [3,4,6,[8][9][10][11]. First, they have to compete against the electronic friction (a velocity-dependent force), and this may require a critical current. Second, the waterwheel effect requires pairs of normal modes degenerate in frequency [3,6,8]. If there is a frequency mismatch, a critical bias may be needed to overcome it. Ramping up the bias to overcome these factors is, notionally, like having to press the accelerator harder to climb a hill.

Nonconservative dynamics in long atomic wires

“…[27] According to the model in Eq. (16), and in agreement with the inset in Fig. 7, the slope should be only weakly dependent on mass at large bias.…”

“…Later we will give an argument to explain the origin of the correction term in brackets in Eq. (16), which will also show that β should be of the order of the electron bandwidth. From the intercepts in the inset in Fig.…”

“…The average force on the other hand contains, among other contributions, the familiar electron wind force [4][5][6][7][8][9]. In recent years the wind force has become the focus of renewed attention due to the realization that it is nonconservative [3,5,[10][11][12][13][14][15][16]. The importance of these nonconservative forces cannot be overestimated.…”

“…Defect-free metallic nanowires are of special interest for these effects. The reason is that the symmetric part of the current-induced contribution to the dynamical response matrix [16] vanishes to lowest order in the bias. This symmetric part is controlled by the real part of the electronic density matrix in the real space representation.…”

Current-induced forces: a simple derivation

“…These problems are being investigated by a growing number of researchers [8][9][10][11][12][13] with further questions being uncovered all the time. However, the physical -and to an extent mathematical -understanding of forces due to current remains a challenging subject, for a simple reason.…”