Tight-binding simulation of current-carrying nanostructures

The tight-binding (TB) approach to the modelling of electrical conduction in small structures is introduced. Different equivalent forms of the TB expression for the electrical current in a nanoscale junction are derived. The use of the formalism to calculate the current density and local potential is illustrated by model examples. A first-principles time-dependent TB formalism for calculating current-induced forces and the dynamical response of atoms is presented. An earlier expression for current-induced forces under steady-state conditions is generalized beyond local charge neutrality and beyond orthogonal TB. Future directions in the modelling of power dissipation and local heating in nanoscale conductors are discussed.

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals, This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.