Lanczos-adapted time evolution for open boundary quantum transport

We increase the efficiency of a recently proposed time integration scheme for time dependent quantum transport by using the Lanczos method for time evolution. We illustrate our modified scheme in terms of a simple one dimensional model. Our results show that the Lanczos-adapted scheme gives a large increase in numerical efficiency, and is an advantageous route for numerical time integration in ab-initio treatment of open boundary quantum transport phenomena.Comment: 11 pages, 1 figur

Theory of Auger core-valence-valence processes in simple metals. II. Dynamical and surface effects on Auger line shapes

ABSTRACT: Auger CVV spectra of simple metals are generally believed to be well described by one-electronlike theories in the bulk which account for matrix elements and, in some cases, also static core-hole screening effects. We present here detailed calculations on Li, Be, Na, Mg, and Al using selfconsistent bulk wave functions and proper matrix elements. The resulting spectra differ markedly from experiment and peak at too low energies. To explain this discrepancy we investigate effects of the surface and dynamical effects of the sudden disappearance of the core hole in the final state. To study core-hole effects we solve Mahan —Nozieres —De Dominicis (MND) model numerically over the entire band. The core-hole potential and other parameters in the MND model are determined by self-consistent calculations of the core-hole impurity. The results are compared with simpler approximations based on the final-state rule due to von Barth and Grossmann. To study surface and mean-free-path effects we perform slab calculations for Al but use a simpler infinite-barrier model in the remaining cases. The model reproduces the slab spectra for Al with very good accuracy. .In all cases investigated either the effects of the surface or the effects of the core hole give important modifications and a much improved agreement with experiment

Theory of auger core-valence-valence processes in simple metals. I. Total yields and core-level lifetime widths

ABSTRACT: There is a considerable disagreement in the literature on the description of lifetime effects arising from core-valence transitions in solids. We calculate here Auger and radiative widths of shallow core levels in Li, Be, Na, Mg, and Al with use of principles consistent with dynamical theories of secondary-emission processes developed earlier. The lifetime has no simple relation to the usual self-energy but is instead directly related to emission yields. The problem of choosing reliable approximations for Auger rates and matrix elements is analyzed theoretically and computationally. We also comment on some earlier approaches. Much of our discussion pertains also to calculations of Auger line shapes from first principles. For long hole lifetimes the total and partial level widths obey an initial-state rule and follow from wave functions perturbed by a static core hole. To obtain these impurity wave .functions we perform self-consistent supercell calculations. The core-hole screening increases the Auger rates by factors of the order 2—4 compared with results from ground-state orbitals but has never been properly included before. The width of the 1s level in Li is rather accurately known because it monitors large effects of incomplete lattice relaxation. For Li we obtain here a width 17 meV in excellent agreement with the value 16 meV deduced earlier from measurements by Callcott et al

Classical Nuclear Motion in Quantum Transport

An ab initio quantum-classical mixed scheme for the time evolution of electrode-device-electrode systems is introduced to study nuclear dynamics in quantum transport. Two model systems are discussed to illustrate the method. Our results provide the first example of current-induced molecular desorption as obtained from a full time-dependent approach and suggest the use of ac biases as a way to tailor electromigration. They also show the importance of non-adiabatic effects for ultrafast phenomena in nanodevices.Comment: 5 pages, 3 figure

Zeno-clocking the Auger decay

A tenet of time-resolved spectroscopy is -faster laser pulses for shorter timescales- . Here we suggest turning this paradigm around, and slow down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.Comment: 5 pages, 4 figures, supplemental material provide

Photoemission Beyond the Sudden Approximation

The many-body theory of photoemission in solids is reviewed with emphasis on methods based on response theory. The classification of diagrams into loss and no-loss diagrams is discussed and related to Keldysh path-ordering book-keeping. Some new results on energy losses in valence-electron photoemission from free-electron-like metal surfaces are presented. A way to group diagrams is presented in which spectral intensities acquire a Golden-Rule-like form which guarantees positiveness. This way of regrouping should be useful also in other problems involving spectral intensities, such as the problem of improving the one-electron spectral function away from the quasiparticle peak.Comment: 18 pages, 11 figure

Time-Dependent Partition-Free Approach in Resonant Tunneling Systems

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in order to deal with the time-dependent current response of a resonant tunneling system. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No fictitious partitions are used. Besides the steady-state responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under what circumstances a steady-state current develops and compare our result with the one obtained in the partitioned scheme. We prove a Theorem of asymptotic Equivalence between the two schemes for arbitrary time-dependent disturbances. We also show that the steady-state current is independent of the history of the external perturbation (Memory Loss Theorem). In the so called wide-band limit an analytic result for the time-dependent current is obtained. In the interacting case we propose an exact non-equilibrium Green function approach based on Time Dependent Density Functional Theory. The equations are no more difficult than an ordinary Mean Field treatment. We show how the scattering-state scheme by Lang follows from our formulation. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is obtained. As an example the time-dependent current response is calculated in the Random Phase Approximation.Comment: final version, 18 pages, 9 figure

Importance of vertex corrections for obtaining correct selection rules in the theory of photoemission

It is shown that the commonly used approximation for the no-loss angle-resolved photocurrent from solids in general violates the optical selection rules if the final-state inverse low-energy electron diffraction orbital is taken to be damped. The violations occur in the velocity formula, which is inconsistent with the corresponding and commonly used acceleration formula in which the matrix elements are evaluated with respect to the gradient of the one-electron potential. It has recently been shown that, in a correct description of the no-loss photocurrent, the bare matrix elements should be replaced by the appropriate vector-coupling vertex function. We demonstrate that this modification is needed in order to have correct selection rules and consistency between the velocity and acceleration formulas for photoemission and photoabsorption. Our formalism further allows us to interpret the commonly used acceleration formula in terms of a well-defined approximation which leaves out local-field effects, and to give approximations which obey the selection rules