# Dr. Tchavdar Todorov

## Reader in Applied Mathematics and Theoretical Physics

Rm: 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

### Degrees, Awards and Honours

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

### Interests

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

### Most Recent Publications

- 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 dynamics in long atomic wireshttp://dx.doi.org/10.1557/opl.2015.197,
*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. - Current-induced forces: a simple derivationhttp://dx.doi.org/10.1103/PhysRevB.90.115430,
*European Journal of Physics*, 2014,**35**, No. 6, pp. 065004**doi:**10.1088/0143-0807/35/6/065004**Abstract**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

### All of Tchavdar's publications

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