DBB.01.011

+44 (0) 28 9097 6030

t.todorov@qub.ac.uk

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

**2003 |**Maxwell Medal and Prize (Institute of Physics, 2003)

- Transport in nanoscale conductors
- Current-induced forces and current-driven atomic motion
- Time-dependent tight binding
- Electron-nuclear dynamics

- Electron-phonon thermalization in a scalable method for real-time quantum dynamics,
*Physical Review B*, 2016,**93**, No. 2**doi:**10.1103/PhysRevB.93.024306**Abstract****Full Text**We present a quantum simulation method that follows the dynamics of out-of-equilibrium many-body systems of electrons and oscillators in real time. Its cost is linear in the number of oscillators and it can probe time scales from attoseconds to hundreds of picoseconds. Contrary to Ehrenfest dynamics, it can thermalize starting from a variety of initial conditions, including electronic population inversion. While an electronic temperature can be defined in terms of a nonequilibrium entropy, a Fermi-Dirac distribution in general emerges only after thermalization. These results can be used to construct a kinetic model of electron-phonon equilibration based on the explicit quantum dynamics. - Efficient simulations with electronic open boundarieshttp://dx.doi.org/10.1103/PhysRevB.93.024306,
*Physical Review B*, 2016,**94**, pp. 075118**doi:**10.1103/PhysRevB.94.075118**Abstract**We present a reformulation of the hairy-probe method for introducing electronic open boundaries that is appropriate for steady-state calculations involving nonorthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms and a perfect nonorthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean interlevel spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current. - Length Matters: Keeping Atomic Wires in Checkhttp://dx.doi.org/10.1103/PhysRevB.94.075118,
*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.

* "If we take the view that quantisation of energy levels, tunnelling and
interference are where quantum mechanics departs most violently
from classical notions, we may ask where do the two come closest?
Nowhere is this proximity more tangible than in the realm of
particle interactions."
* Undated, Anon

This we can put to a simple test. In a random array of barriers, a combination
of

quantisation, tunnelling and interference generates trapped quantum states:

But couple this to another set of degrees of freedom, and the picture washes out:

Without ** electron-phonon interactions ** life would crash. For
starters we’d lose our sense of smell (PRL ** 98 ** (2007) 038101), not

always a bad thing of course. Electrical and electronic equipment
would seize up. Even if we could keep electrical appliances going,

we wouldn't be getting the energy in the forms and places needed.
On the downside, the laptop armies at meetings are among

today's biggest energy wasters. E-phonon scattering is how electrons
and atomic vibrations exchange energy and momentum,

which often controls charge and energy transport in molecular
and condensed matter systems, and enforces thermal equilibrium.

Despite their fundamental role e-phonon interactions remain a challenge.
Stepping beyond the Born-Oppenheimer approximation

opens a many-body problem (even ignoring e-e interactions).
The most difficult are situations involving the simultaneous coupled

dynamics of the two subsystems. We have worked on this problem in
nanoscale conductors and systems under irradiation, with

support by EPSRC and the Leverhulme Trust. In both contexts -
"molecular electronics" and radiation damage - electrons and

the ionic motion can be driven very far out of equilibrium,
resulting in violent momentum and energy exchange. Recently we have

developed a method for coupled e-phonon dynamics that can reach significant
size- and time-scales. Take a 2d quantum dot

on a substrate,
following electronic excitation. We can then track the relaxation
back towards equilibrium in time. The process

can be monitored via the dot state occupancies. Notice the interplay between
transitions. A vital process in this is spontaneous

phonon emission.
It's often the hardest to capture, and is where
mean-field electron-nuclear dynamics breaks down.

* Valerio Rizzi, Tchavdar Todorov, Jorge Kohanoff and Alfredo Correa, *
PRB ** 93 ** (2016) 024306