Dr. Tchavdar Todorov
Reader in Applied Mathematics and Theoretical Physics
+44 (0) 28 9097 6030
Atomistic Simulation Centre
School of Mathematics
Queen's University Belfast
Belfast BT7 1NN
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
- 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.