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

Surface Screening Charge and Effective Charge

The charge on an atom at a metallic surface in an electric field is defined as the field-derivative of the force on the atom, and this is consistent with definitions of effective charge and screening charge. This charge can be found from the shift in the potential outside the surface when the atoms are moved. This is used to study forces and screening on surface atoms of Ag(001) c$(2\times 2)$ -- Xe as a function of external field. It is found that at low positive (outward) fields, the Xe with a negative effective charge of -0.093 $|{e}|$ is pushed into the surface. At a field of 2.3 V \AA$^{-1}$ the charge changes sign, and for fields greater than 4.1 V \AA$^{-1}$ the Xe experiences an outward force. Field desorption and the Eigler switch are discussed in terms of these results.Comment: 4 pages, 1 figure, RevTex (accepted by PRL

An embedding scheme for the Dirac equation

An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded Hamiltonian is equal to the Green function for the entire system in region I. Application of the method is illustrated for the problem of a hydrogen atom in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure using basis sets that satisfy kinetic balance.Comment: 16 pages, 5 figure