Dr. Tchavdar Todorov

Reader in Applied Mathematics and Theoretical Physics


+44 (0) 28 9097 6030

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

Degrees, Awards and Honours

  • 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

Most Recent Publications

  1. 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.

  2. 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.

  3. 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.

All of Tchavdar's publications


"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