136 research outputs found
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 -- 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
is pushed into the surface. At a field of 2.3 V \AA the charge
changes sign, and for fields greater than 4.1 V \AA 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
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