Landauer Theory, Inelastic Scattering and Electron Transport in Molecular Wires

In this paper we address the topic of inelastic electron scattering in mesoscopic quantum transport. For systems where only elastic scattering is present, Landauer theory provides an adequate description of transport that relates the electronic current to single-particle transmission and reflection probabilities. A formalism proposed recently by Bonca and Trugman facilitates the calculation of the one-electron transmission and reflection probabilities for inelastic processes in mesoscopic conductors connected to one-dimensional ideal leads. Building on their work, we have developed a self-consistent procedure for the evaluation of the non-equilibrium electron distributions in ideal leads connecting such mesoscopic conductors to electron reservoirs at finite temperatures and voltages. We evaluate the net electronic current flowing through the mesoscopic device by utilizing these non-equilibrium distributions. Our approach is a generalization of Landauer theory that takes account of the Pauli exclusion principle for the various competing elastic and inelastic processes while satisfying the requirement of particle conservation. As an application we examine the influence of elastic and inelastic scattering on conduction through a two site molecular wire with longitudinal phonons using the Su-Schrieffer-Heeger model of electron-phonon coupling.Comment: 25 pages, 8 figure

Transmission Properties of the oscillating delta-function potential

We derive an exact expression for the transmission amplitude of a particle moving through a harmonically driven delta-function potential by using the method of continued-fractions within the framework of Floquet theory. We prove that the transmission through this potential as a function of the incident energy presents at most two real zeros, that its poles occur at energies $n\hbar\omega+\varepsilon^*$ ($0<Re(\varepsilon^*)<\hbar\omega$), and that the poles and zeros in the transmission amplitude come in pairs with the distance between the zeros and the poles (and their residue) decreasing with increasing energy of the incident particle. We also show the existence of non-resonant "bands" in the transmission amplitude as a function of the strength of the potential and the driving frequency.Comment: 21 pages, 12 figures, 1 tabl

Electron correlation effects in a wide channel from the ν=1\nu =1 quantum Hall edge states

The spatial behavior of Landau levels (LLs) for the $nu=1$ quantum Hall regime at the edge of a wide channel is studied in a self-consistent way by using a generalized local density approximation proposed here. Both exchange interaction and strong electron correlations, due to edge states, are taken into account. They essentially modify the spatial behavior of the occupied lowest spin-up LL in comparison with that of the lowest spin-down LL, which is totally empty. The contrast in the spatial behavior can be attributed to a different effective one-electron lateral confining potentials for the spin-split LLs. Many-body effects on the spatially inhomogeneous spin-splitting are calculated within the screened Hartree-Fock approximation. It is shown that, far from the edges, the maximum activation energy is dominated by the gap between the Fermi level and the bottom of the spin-down LL, because the gap between the Fermi level and the spin-up LL is much larger. In other words, the maximum activation energy in the bulk of the channel corresponds to a highly asymmetric position of the Fermi level within the gap between spin-down and spin-up LLs in the bulk. We have also studied the renormalization of the edge-state group velocity due to electron correlations. The results of the present theory are in line with those suggested and reported by experiments on high quality samples.Comment: 9 pages, 4 figure

Influence of typical environments on quantum processes

We present the results of studying the influence of different environmental states on the coherence of quantum processes. We choose to discuss a simple model which describe two electronic reservoirs connected through tunneling via a resonant state. The model could, e.g., serve as an idealization of inelastic resonant tunneling through a double barrier structure. We develop Schwinger's closed time path formulation of non-equilibrium quantum statistical mechanics, and show that the influence of the environment on a coherent quantum process can be described by the value of a generating functional at a specific force value, thereby allowing for a unified discussion of destruction of phase coherence by various environmental states: thermal state, classical noise, time dependent classical field, and a coherent state. The model allows an extensive discussion of the influence of dissipation on the coherent quantum process, and expressions for the transmission coefficient are obtained in the possible limits.Comment: 46 pages, 11 post script figures. Accepted for publication in Physical Review

Ensemble density functional theory of the fractional quantum Hall effect

We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with semiclassical and Hartree-Fock calculations, and with small system numerical diagonalizations. This establishes the usefulness of density functional theory to study the fractional quantum Hall effect, which opens up the possibility of studying inhomegeneous systems with many more electrons than has heretofore been possible.Comment: Improved discussion of ensemble density functional theory. 4 pages plus 3 postscript figures, uses latex with revtex. Contact [email protected]