DBB.01.021

+44 (0) 28 9097 3369

d.dundas@qub.ac.uk

Atomistic Simulation Centre School of Mathematics and Physics Queen's University Belfast University Road Belfast BT7 1NN Northern Ireland

- Length Matters: Keeping Atomic Wires in Check,
*MRS Proceedings*, 2015,**1753****doi:**10.1557/opl.2015.197**Abstract**Dynamical effects of non-conservative forces in long, defect free atomic wires are investigated. Current flow through these wires is simulated and we find that during the initial transient, the kinetic energies of the ions are contained in a small number of phonon modes, closely clustered in frequency. These phonon modes correspond to the waterwheel modes determined from preliminary static calculations. The static calculations allow one to predict the appearance of non-conservative effects in advance of the more expensive real-time simulations. The ion kinetic energy redistributes across the band as non-conservative forces reach a steady state with electronic frictional forces. The typical ion kinetic energy is found to decrease with system length, increase with atomic mass, and its dependence on bias, mass and length is supported with a pen and paper model. This paper highlights the importance of non-conservative forces in current carrying devices and provides criteria for the design of stable atomic wires. - Nonconservative current-driven dynamics: beyond the nanoscalehttp://dx.doi.org/10.1557/opl.2015.197,
*Beilstein Journal of Nanotechnology*, 2015,**6**, pp. 2140**doi:**10.3762/bjnano.6.219**Abstract****Full Text**Long metallic nanowires combine crucial factors for nonconservative current-driven atomic motion. These systems have degenerate vibrational frequencies, clustered about a Kohn anomaly in the dispersion relation, that can couple under current to form nonequilibrium modes of motion growing exponentially in time. Such motion is made possible by nonconservative current-induced forces on atoms, and we refer to it generically as the waterwheel effect. Here the connection between the waterwheel effect and the stimulated directional emission of phonons propagating along the electron flow is discussed in an intuitive manner. Nonadiabatic molecular dynamics show that waterwheel modes self-regulate by reducing the current and by populating modes in nearby frequency, leading to a dynamical steady state in which nonconservative forces are counter-balanced by the electronic friction. The waterwheel effect can be described by an appropriate effective nonequilibrium dynamical response matrix. We show that the current-induced parts of this matrix in metallic systems are long-ranged, especially at low bias. This nonlocality is essential for the characterisation of nonconservative atomic dynamics under current beyond the nanoscale. - Nonconservative dynamics in long atomic wireshttp://dx.doi.org/10.3762/bjnano.6.219,
*Physical Review B*, 2014,**90**, pp. 115430**doi:**10.1103/PhysRevB.90.115430**Abstract**The effect of nonconservative current-induced forces on the ions in a defect-free metallic nanowire is investigated using both steady-state calculations and dynamical simulations. Nonconservative forces were found to have a major influence on the ion dynamics in these systems, but their role in increasing the kinetic energy of the ions decreases with increasing system length. The results illustrate the importance of nonconservative effects in short nanowires and the scaling of these effects with system size. The dependence on bias and ion mass can be understood with the help of a simple pen and paper model. This material highlights the benefit of simple preliminary steady-state calculations in anticipating aspects of brute-force dynamical simulations, and provides rule of thumb criteria for the design of stable quantum wires.

#### Ultra-fast electron and photon driven dynamics in molecular systems

The interaction of molecular systems with ultra short laser pulses provide fundamental examples of complex quantum many body systems driven far from equilibrium. A highly non perturbative and non adiabatic coupling exists between electronic and nuclear degrees of freedom which induces both charge and energy flow within the molecule. These charge and energy transfer processes occur on the femtosecond timescale, and are of extreme importance in the design of electronic devices, probes and sensors, and in the areas of condensed matter and plasma physics, medicine and biochemistry. The development of non adiabatic quantum approaches is therefore one of the great challenges in Physics. The challenge comes about through the diversity of time scales that occur in the problem. These time scales range from a few femtosecond for electron transfer through tens of femtoseconds for excitation processes to hundreds of femtoseconds characterizing the ionic motion. All these processes need to be described within a consistent dynamical picture.

We have developed a number of approaches for describing the inteaction of molecules using both full quantum descriptions of electron and ions for small molecules and mixed, quantum classical approaches for large molecules.

**Quantum electron-ion dynamics of small molecules**For one- and two-electron diatomic molecules such as H

_{2}^{+}and H_{2}we can treat both the electronic and vibrational degrees of freedom exactly through the solution of the time-dependent Schroedinger equation (TDSE), assuming that the laser light is linearly polarised along the intermolecular axis. Studying such systems interacting with ultrashort intense laser pulse allows us to gain an understanding of the fundamental roles of electron-electron and electron-ion interactions in ultrafast processes and can act as a benchmark for high-precision laboratory experiment.We have developed computer codes based on a mixed Lagrange mesh and finite difference approach for solving the TDSE for these molecules. These include a code called THeREMIN (vibraTing HydRogEn Molecular IoN) for describing H

_{2}^{+}and a code called H2MOL for describing H_{2}.This work is being carried out with Alejandro de la Calle.

**Pre-ionization dynamics of H**_{2}^{+}by an ultrashort laser pulse

Dissociation of H_{2}^{+}by a 6-cycle linearly polarized Ti:sapphire laser pulse. The molecule lies along the z-axis with the laser polarization aligned along this axis. The TDSE is solved in cylindrical coordinates with -150 ≤ z ≤ 150, 0 ≤ ρ ≤ 100, 0 ≤ R ≤ 20. In the plot the ρ coordiante has been integrated over and we focus on that part of the grid neat the atoms. We see electron wavepacket responding in antiphase to the field with very little ionization occuring. After the pulse has finished, we see wavepackets moving out in R which is indicative of dissociation.**Relevant Papers****Title:**Dissociative ionization of molecules in intense laser fields**Author(s):**Dundas D., Meharg K.J., McCann J.F., Taylor K.T.*European Physical Journal D*,**26**, No. 1, pp. 51-57 (OCT 2003)**Title:**Efficient grid treatment of the ionization dynamics of laser-driven H-2(+)**Author(s):**Dundas D.*Physical Review A*,**65**, No. 2, Art. No. 023408 (FEB 2002)

**Quantum-classical dynamics of large molecules**The basis of this research is a time dependent density functional theory approach implemented in a real space, massively parallel computer code called EDAMAME (Ehrenfest DynAMics on Adaptive MEshes). This code was developed in both the ASC and CTAMOP.

The aim of this research is to develop an experimental and theoretical capability that will lead to a novel method for peptide sequencing using ultrashort laser pulses. This work is being carried out with Abi Wardlow, in collaboration with Dr Jason Greenwood of the Centre for Plasma Physics at QUB.

**Ionization of Benzene by an intense, ultrashort laser pulse**

Ionization of benzene by a 5-cycle Ti:sapphire laser pulse. The benzene molecule lies in the plane and the laser pulse is linearly-polarised with the polarization direction horizontal in the plane. The laser wavelength is λ = 780 nm and its peak intensity is I = 4.0x10^{14}W/cm^{2}. Ionizing electron wavepacket is emitted each half-cycle, in anti-phase to the field, as the laser electric field strength passes through maxima and minima.**Relevant Papers****Title:**Multielectron effects in high harmonic generation in N2 and benzene: Simulation using a non-adiabatic quantum molecular dynamics approach for laser-molecule interactions**Author(s):**Dundas D.*Journal of Chemical Physics*,**136**, No. 19, pp. 194303-1-194303-17 (MAY 2012)**Title:**Molecular effects in the ionization of N2, O2, and F2 by intense laser fields**Author(s):**Dundas D., Rost J.-M.*Physical Review A*,**71**, No. 1, Art. No. 013421 (JAN 2005)

#### Non-conservative current-induced forces in nanoscale devices

We work on the real-time simulation of current flow in these systems, and of the dynamics of the atoms driven by the huge current densities possible in atomic wires. A recent breakthrough was to prove theoretically that the forces on atoms that current flow exerts are non-conservative, and to simulate the resultant operation of a one-atom 'waterwheel'. This work was featured in two News and Views articles in the Nature Journals and sparked off experimental and theoretical interest internationally.

**Atomic waterwheels**

An open-boundary non-adiabatic molecular dynamics simulation of the corner atom in a bent atomic wire. The current in the wire is in the region of 70 μ A. The atom is driven in an expanding orbit by the non-conservative current-induced force on it. Its kinetic energy grows exponentially in time, till other factors kick in to slow it down.**Relevant Papers****Title:**Current-driven atomic waterwheels**Author(s):**Dundas D., McEniry E.J., Todorov T.N.*Nature Nanotechnology*,**4**, No. 2, pp. 99-102 (2009)**Title:**An ignition key for atomic-scale engines**Author(s):**Dundas D., Cunningham B., Buchanan C., Terasawa A., Anthony T Paxton A.T., Todorov T.N.*Journal of Physics: Condensed Matter*,**24**, pp. 402203-1-402203-6 (2012)