Time-dependent embedding: surface electron emission

An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of space, the region of physical interest, the embedding potential ensuring that the wavefunction satisfies the correct boundary conditions for matching on to the rest of the system. This is applied to a study of the excitation of electrons at a metal surface, represented by a one-dimensional model potential for Cu(111). Time-dependent embedding potentials are derived for replacing the bulk substrate, and the image potential and vacuum region outside the surface, so that the calculation of electron excitation by a surface perturbation can be restricted to the surface itself. The excitation of the Shockley surface state and a continuum bulk state is studied, and the time-structure of the resulting currents analysed. Non-linear effects and the time taken for the current to arrive outside the surface are discussed. The method shows a clear distinction between emission from the localized surface state, where the charge is steadily depleted, and the extended continuum state where the current emitted into the vacuum is compensated by current approaching the surface from the bulk.Comment: 15 figure

Time-dependent embedding

A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\"odinger equation. Results are presented for a one-dimensional model of an atom in a time-varying electric field, the surface excitation of this model atom at a jellium surface in an external electric field, and the surface excitation of a bulk state.Comment: 31 pages, 13 figure

An embedding potential definition of channel functions

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluated over the interface. Using the new channel functions, a well-known result for the total transmission through the conductor system is simply derived.Comment: 14 pages, 2 figure

An augmented space recursion study of the electronic structure of rough epitaxial overlayers

In this communication we propose the use of the Augmented Space Recursion as an ideal methodology for the study of electronic and magnetic structures of rough surfaces, interfaces and overlayers. The method can take into account roughness, short-ranged clustering effects, surface dilatation and interdiffusion. We illustrate our method by an application of Fe overlayer on Ag (100) surface.Comment: 22 pages, Latex, 6 postscript figure

Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems

Core reconstruction in pseudopotential calculations

A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {\bf 14}, 3795 (1981)]. In this method the core region is \emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an analysis of the errors introduced in constructing this from a set of numerical eigenstates is given. Results are presented for an all-electron reconstruction of bulk aluminium, for both the charge density and the density of states.Comment: 14 pages, 5 figure

Dynamic image potential at an Al(111) surface

We evaluate the electronic self-energy Sigma(E) at an Al(111) surface using the GW space-time method. This self-energy automatically includes the image potential V-im not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure