Title: High-order-harmonic generation in benzene with linearly and circularly polarized laser pulses
Author(s): Wardlow A., Dundas D.
Physical Review A, 93, pp. 023428- (25 February 2016)
High-order-harmonic generation in benzene is studied using a mixed quantum-classical approach in which the electrons are described using time-dependent density-functional theory while the ions move classically. The interaction with both linearly and circularly polarized infrared (λ=800 nm) laser pulses of duration of ten cycles (26.7 fs) is considered. The effect of allowing the ions to move is investigated as is the effect of including self-interaction corrections to the exchange-correlation functional. Our results for circularly polarized pulses are compared with previous calculations in which the ions were kept fixed and self-interaction corrections were not included, while our results for linearly polarized pulses are compared with both previous calculations and experiment. We find that even for the short-duration pulses considered here, the ionic motion greatly influences the harmonic spectra. While ionization and ionic displacements are greatest when linearly polarized pulses are used, the response to circularly polarized pulses is almost comparable, in agreement with previous experimental results.
Title: Length Matters: Keeping Atomic Wires in Check
Author(s): Cunningham B., Todorov T.N., Dundas D.
MRS Proceedings, 1753 (2015)
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.
Title: Nonconservative current-driven dynamics: beyond the nanoscale
Author(s): Cunningham B., Todorov T.N., Dundas D.
Beilstein Journal of Nanotechnology, 6, pp. 2140-2147 (13 November 2015)
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.
Title: Nonconservative dynamics in long atomic wires
Author(s): Cunningham B., Todorov T.N., Dundas D.
Physical Review B, 90, pp. 115430 - (24 September 2014)
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.
Title: Current-induced forces: a simple derivation
Author(s): Todorov T.N., Dundas D., Lü J., Brandbyge M., Hedegård P.
European Journal of Physics, 35, No. 6, pp. 065004- (02 September 2014)
We revisit the problem of forces on atoms under current in nanoscale conductors. We derive and discuss the five principal kinds of force under steady-state conditions from a simple standpoint that—with the help of background literature—should be accessible to physics undergraduates. The discussion aims at combining methodology with an emphasis on the underlying physics through examples. We discuss and compare two forces present only under current—the non-conservative electron wind force and a Lorentz-like velocity-dependent force. It is shown that in metallic nanowires both display significant features at the wire surface, making it a candidate for the nucleation of current-driven structural transformations and failure. Finally we discuss the problem of force noise and the limitations of Ehrenfest dynamics
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)
A mixed quantum-classical approach is introduced which allows the dynamical response of molecules driven far from equilibrium to be modeled. This method is applied to the interaction of molecules with intense, short-duration laser pulses. The electronic response of the molecule is described using time-dependent density functional theory (TDDFT) and the resulting Kohn-Sham equations are solved numerically using finite difference techniques in conjunction with local and global adaptations of an underlying grid in curvilinear coordinates. Using this approach, simulations can be carried out for a wide range of molecules and both all-electron and pseudopotential calculations are possible. The approach is applied to the study of high harmonic generation in N2 and benzene using linearly polarized laser pulses and, to the best of our knowledge, the results for benzene represent the first TDDFT calculations of high harmonic generation in benzene using linearly polarized laser pulses. For N2 an enhancement of the cut-off harmonics is observed whenever the laser polarization is aligned perpendicular to the molecular axis. This enhancement is attributed to the symmetry properties of the Kohn-Sham orbital that responds predominantly to the pulse. In benzene we predict that a suppression in the cut-off harmonics occurs whenever the laser polarization is aligned parallel to the molecular plane. We attribute this suppression to the symmetry-induced response of the highest-occupied molecular orbital.
Title: Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach
Author(s): Lü J.T., Brandbyge M., Hedegård P., Todorov T.N., Dundas D.,
Physical Review B, 85, pp. 245444- (25 June 2012)
We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway “waterwheel” modes) and investigate the signature of these in the Raman signals.
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)
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.
Title: Nonconservative current-induced forces: A physical interpretation
Author(s): Todorov T.N., Dundas D., Paxton A.T., Horsfield A.P.
Beilstein Journal of Nanotechnology, 2, pp. 727-733 (2011)
We give a physical interpretation of the recently demonstrated nonconservative nature of interatomic forces in current-carrying nanostructures. We start from the analytical expression for the curl of these forces, and evaluate it for a point defect in a current-carrying system. We obtain a general definition of the capacity of electrical current flow to exert a nonconservative force, and thus do net work around closed paths, by a formal noninvasive test procedure. Second, we show that the gain in atomic kinetic energy over time, generated by nonconservative current-induced forces, is equivalent to the uncompensated stimulated emission of directional phonons. This connection with electronâphonon interactions quantifies explicitly the intuitive notion that nonconservative forces work by angular momentum transfer.
Title: Nonconservative generalized current-induced forces
Author(s): Todorov T.N., Dundas D., McEniry E.J.
Physical Review B, 81, No. 7, Art. No. 075416 (2010)
A recent result for the curl of forces on ions under steady-state current in atomic wires with noninteracting electrons is extended to generalized forces on classical degrees of freedom in the presence of mean-field electron-electron screening. Current is described within a generic multiterminal picture, forces within the Ehrenfest approximation, and screening within an adiabatic, but not necessarily spatially local, mean-field picture.
Title: Modelling non-adiabatic processes using correlated electron-ion dynamics
Author(s): McEniry E.J., Wang Y., Dundas D., Todorov T.N., Stella L., Miranda R.P., Fisher A.J., Horsfield A.P., Race C.P., Mason D.R., Foulkes W.M.C., Sutton A.P.
European Physical Journal B , 77, No. 3, pp. 305-329 (October 2010)
Here we survey the theory and applications of a family of methods (correlated electron-ion dynamics, or CEID) that can be applied to a diverse range of problems involving the non-adiabatic exchange of energy between electrons and nuclei. The simplest method, which is a paradigm for the others, is Ehrenfest Dynamics. This is applied to radiation damage in metals and the evolution of excited states in conjugated polymers. It is unable to reproduce the correct heating of nuclei by current carrying electrons, so we introduce a moment expansion that allows us to restore the spontaneous emission of phonons. Because of the widespread use of Non-Equilibrium Green's Functions for computing electric currents in nanoscale systems, we present a comparison of this formalism with that of CEID with open boundaries. When there is strong coupling between electrons and nuclei, the moment expansion does not converge. We thus conclude with a reworking of the CEID formalism that converges systematically and in a stable manner.
Title: Current-driven atomic waterwheels
Author(s): Dundas D., McEniry E.J., Todorov T.N.
Nature Nanotechnology, 4, No. 2, pp. 99-102 (2009)
A current induces forces on atoms inside the conductor that carries it. It is now possible to compute these forces from scratch, and to perform dynamical simulations of the atomic motion under current. One reason for this interest is that current can be a destructive force—it can cause atoms to migrate, resulting in damage and in the eventual failure of the conductor. But one can also ask, can current be made to do useful work on atoms? In particular, can an atomic-scale motor be driven by electrical current, as it can be by other mechanisms? For this to be possible, the current-induced forces on a suitable rotor must be non-conservative, so that net work can be done per revolution. Here we show that current-induced forces in atomic wires are not conservative and that they can be used, in principle, to drive an atomic-scale waterwheel.
Title: Current-assisted cooling in atomic wires
Author(s): McEniry E.J., Todorov T.N., Dundas D.,
Journal of Physics: Condensed Matter, 21, No. 19 (2009)
The effects of inelastic interactions between current-carrying electrons and vibrational modes of a nanoscale junction are a major limiting factor on the stability of such devices. A method for dynamical simulation of inelastic electron-ion interactions in nanoscale conductors is applied to a model system consisting of an adatom bonded to an atomic wire. It is found that the vibrational energy of such a system may decrease under bias, and furthermore that, as the bias is increased, the rate of cooling, within certain limits, will increase. This phenomenon can be understood qualitatively through low-order perturbation theory, and is due to the presence of an anti-resonance in the transmission function of the system at the Fermi level. Such current-assisted cooling may act as a stabilization mechanism, and may form the basis for a nanoscale cooling 'fan'.
Title: Inelastic quantum transport in nanostructures: The self-consistent Born approximation and correlated electron-ion dynamics
Author(s): McEniry E.J., Frederiksen T., Todorov T.N., Dundas D., Horsfield A.P.,
Physical Review B, 78, No. 3 (2008)
A dynamical method for inelastic transport simulations in nanostructures is compared to a steady-state method based on nonequilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits an enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations where differences begin to emerge.
Title: Correlated electron-ion dynamics in metallic systems
Author(s): Horsfield A.P., Finnis M., Foulkes M., LePage J., Mason D., Race C., Sutton A.P., Bowler D.R., Fisher A.J., Miranda R., Stella L., Stoneham A.M., Dundas D., McEniry E., Todorov T.N., Sanchez C.G.,
Computational Materials Science, 44, No. 1, pp. 16-20 (November 2008)
In this paper we briefly discuss the problem of simulating non-adiabatic processes in systems that are usefully modelled using molecular dynamics. In particular we address the problems associated with metals, and describe two methods that can be applied: the Ehrenfest approximation and correlated electron-ion dynamics (CEID). The Ehrenfest approximation is used to successfully describe the friction force experienced by an energetic particle passing through a crystal, but is unable to describe the heating of a wire by an electric current. CEID restores the proper heating. (C) 2008 Elsevier B.V. All rights reserved.
Title: Dynamical simulation of inelastic quantum transport
Author(s): McEniry E.J., Bowler D.R., Dundas D., Horsfield A.P., Sanchez C.G., Todorov T.N.
Journal Of Physics-Condensed Matter, 19, No. 19, Art. No. 196201 (MAY 16 2007)
A method for correlated quantum electron-ion dynamics is combined with a method for electronic open boundaries to simulate in real time the heating, and eventual equilibration at an elevated vibrational energy, of a quantum ion under current flow in an atomic wire, together with the response of the current to the ionic heating. The method can also be used to extract inelastic current voltage corrections under steady-state conditions. However, in its present form the open-boundary method contains an approximation that limits the resolution of current-voltage features. The results of the simulations are tested against analytical results from scattering theory. Directions for the improvement of the method are summarized at the end.
Title: Multiphoton double ionization of atoms and molecules by FEL XUV light
Author(s): Taylor K.T., Parker J.S., Dundas D., Meharg K.J., Doherty B.J.S., Murphy D.S., McCann J.F.
Journal Of Electron Spectroscopy And Related Phenomena, 144, No. Sp. Iss. SI, pp. 1191-1196 (JUN 2005)
We review recent work carried out in Belfast which handles the few-electron dynamics of atomic and molecular systems exposed to high frequency, high intensity laser fields. The design and application of the quantitatively accurate computational methods is discussed. The Belfast work is illustrated by results for double ionization of helium and the hydrogen molecule by FEL XUV light where in each case the two electrons have been handled in full-dimensionality. (c) 2005 Elsevier B.V. All rights reserved.
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)
In this paper we study the response in time of N2, O2, and F2 to laser pulses having a wavelength of 390 nm. We find single-ionization suppression in O2 and its absence in F2, in accordance with experimental results at λ=800 nm. Within our framework of time-dependent density functional theory we are able to explain deviations from the predictions of intense-field many-body S-matrix theory (IMST). We confirm the connection of ionization suppression with destructive interference of outgoing electron waves from the ionized electron orbital. However, the prediction of ionization suppression, justified within the IMST approach through the symmetry of the highest occupied molecular orbital (HOMO), is not reliable since it turns out that—e.g., in the case of F2—the electronic response to the laser pulse is rather complicated and does not lead to dominant depletion of the HOMO. Therefore, the symmetry of the HOMO is not sufficient to predict ionization suppression. However, at least for F2, the symmetry of the dominantly ionized orbital is consistent with the nonsuppression of ionization.
Title: Accurate and efficient non-adiabatic quantum molecular dynamics approach for laser-matter interactions
Author(s): Dundas D.
Journal Of Physics B-Atomic Molecular And Optical Physics, 37, No. 14, pp. 2883-2901 (JUL 28 2004)
A non-adiabatic quantum molecular dynamics approach for treating the interaction of matter with intense, short-duration laser pulses is developed. This approach, which is parallelized to run on massively-parallel supercomputers, is shown to be both accurate and efficient. Illustrative results are presented for harmonic generation occurring in diatomic molecules using linearly polarized laser pulses.
Title: A discrete time-dependent method for metastable atoms and molecules in intense fields
Author(s): Peng L.Y., McCann J.F., Dundas D., Taylor K.T., Williams I.D.
Journal Of Chemical Physics, 120, No. 21, pp. 10046-10055 (JUN 1 2004)
The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments. (C) 2004 American Institute of Physics.
Title: Dynamic tunnelling ionization of H-+(2) in intense fields
Author(s): Peng L.Y., Dundas D., McCann J.F., Taylor K.T., Williams I.D.
Journal Of Physics B-Atomic Molecular And Optical Physics, 36, No. 18, pp. L295-L302 (SEP 28 2003)
Intense-field ionization of the hydrogen molecular ion by linearly polarized light is modelled by direct solution of the fixed-nuclei time-dependent Schrodinger equation and compared with recent experiments. Parallel transitions are calculated using algorithms which exploit massively parallel computers. We identify and calculate dynamic tunnelling ionization resonances that depend on laser wavelength and intensity, and molecular bond length. Results for lambda similar to 1064 nm are consistent with static tunnelling ionization. At shorter wavelengths lambda similar to 790 nm large dynamic corrections are observed. The results agree very well with recent experimental measurements of the ion spectra. Our results reproduce the single peak resonance and provide accurate ionization rate estimates at high intensities. At lower intensities our results confirm a double peak in the ionization rate as the bond length varies.
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)
Accurate and efficient grid based techniques for the solution of the time-dependent Schrodinger equation for few-electron diatomic molecules irradiated by intense, ultrashort laser pulses are described. These are based on hybrid finite-difference, Lagrange mesh techniques. The methods are applied in three scenarios, namely H-2(+) with fixed internuclear separation, H-2(+) with vibrating nuclei and H-2 with fixed internuclear separation and illustrative results presented.
Title: Laser-driven helium at 780 nm
Author(s): Taylor K.T., Parker J.S., Meharg K.J., Dundas D.
European Physical Journal D, 26, No. 1, pp. 67-71 (OCT 2003)
We briefly review the methods under development at Queen's University Belfast to solve the full-dimensionality time-dependent Schrodinger equation for helium in intense laser fields. We set out the computational challenges involved in performing calculations that handle Ti:sapphire laser light at its fundamental wavelength (similar to780 nm) in comparison to those encountered for 390 nm light. We remark upon the very considerable importance of accurate and reliable calculations at 780 nm and present results for single-ionization of helium at this wavelength.
Title: Laser-driven helium, H-2(+) and H-2
Author(s): Taylor K.T., Parker J.S., Dundas D., Meharg K.J., Moore L.R., McCann J.F.
Journal Of Modern Optics, 50, No. 3-4, pp. 401-422 (JAN 2003)
We review work carried out in recent years at Belfast devoted to handling the dynamics of laser-driven few-electron atomic and molecular systems in full dimensionality with the goal of bringing quantitative discipline to the field. The design and application of quantitatively accurate computational methods are discussed. Electron-electron correlations induced by intense external fields are observed by calculating the position and momentum space distributions of the doubly ionizing two-electron wave packets and the application of the techniques of scientific visualization analysis to such studies is emphasized. Agreement of results obtained with those from recent laboratory experiments is demonstrated. Work in hand and plans for future calculations are outlined.
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)
We implement a parallel, time-dependent hybrid finite-difference Lagrange mesh code to model the electron dynamics of the fixed-nuclei hydrogen molecular ion subjected to intense ultrashort laser Pulses, Ionization rates are calculated and compared with results from a previous finite-difference approach and also with published Floquet results. The sensitivity of the results to the gauge describing the electron-field interaction is studied. Visualizations of the evolving wave packets are also presented in which the formation of a stable bound-state resonance is observed.
Title: Double-electron above threshold ionization of helium
Author(s): Parker J.S., Moore L.R., Meharg K.J., Dundas D., Taylor K.T.
Journal Of Physics B-Atomic Molecular And Optical Physics, 34, No. 3, pp. L69-L78 (FEB 14 2001)
We present calculations of intense-field multiphoton ionization processes in helium at XUV wavelengths. The calculations are obtained from a full-dimensional integration of the two-electron time-dependent Schrodinger equation. A momentum-space analysis of the ionizing two-electron wavepacket reveals the existence of double-electron above threshold ionization (DATI). In momentum-space two distinct forms of DAITI are resolved, namely non-sequential and sequential. In non-sequential DATI correlated electrons resonantly absorb and share energy in integer units of h omega (laser).
Title: Double ionization of helium at 390 um
Author(s): Parker J.S., Moore L.R., Dundas D., Taylor K.T.
Journal Of Physics B-Atomic Molecular And Optical Physics, 33, No. 20, pp. L691-L698 (OCT 28 2000)
We present calculations of single- and double-ionization rates of helium at 390 nm, accurate to within 10%, obtained from a full-dimensional integration of the time-dependent Schrodinger equation. The theoretical results are compared with experimental data at the same wavelength. Excellent agreement is obtained, allowing for likely uncertainties in the experimental determination of laser intensity.
Title: Ionization dynamics of laser-driven H-2(+)
Author(s): Dundas D., McCann J.F., Parker J.S., Taylor K.T.
Journal Of Physics B-Atomic Molecular And Optical Physics, 33, No. 17, pp. 3261-3276 (SEP 14 2000)
We set out aspects of a numerical algorithm used in solving the full-dimensionality time-dependent Schrodinger equation describing the electronic motion of the hydrogen molecular ion driven by an intense, linearly polarized laser pulse aligned along the molecular axis. This algorithm has been implemented within the fixed inter-nuclear separation approximation in a parallel computer code, a brief summary of which is given. Ionization rates are calculated and compared with results from other methods, notably the time-independent Floquet method. Our results compare very favourably with the precise predictions of the Floquet method, although there is some disagreement with other wavepacket calculations. Visualizations of the electron dynamics are also presented in which electron rescattering is observed.