17 research outputs found
Transmission of Renormalized Benzene Circuits
The renormalization equations emerge from a Greenian-matrix solution of the
discretized Schrodinger equation. A by-product of these equations is the
decimation process, which enables substituted-benzenes to be mapped onto
corresponding dimers, that are used to construct the series and parallel
circuits of single-, double- and triple-dimers. The transmittivities of these
circuits are calculated by the Lippmann-Schwinger theory, which yields the
transmission-energy function T(E). The average value of T(E) provides a measure
of the electron transport in the circuit in question. The undulating nature of
the T(E) profiles give rise to resonances (T=1) and anti-resonances (T=0)
across the energy spectrum. Analysis of the structure of the T(E) graphs
highlights the distinguishing features associated with the homo- and
hetero-geneous series and parallel circuits. Noteworthy results include the
preponderance of p-dimers in circuits with high T(E) values, and the fact that
parallel circuits tend to be better transmitters than their series
counterparts.Comment: 32 pages, 14 figures, 1 tabl
Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance
In this paper we derive general relations for the band-structure of an array
of quantum dots and compute its transport properties when connected to two
perfect leads. The exact lattice Green's functions for the perfect array and
with an attached adatom are derived. The expressions for the linear conductance
for the perfect array as well as for the array with a defect are presented. The
calculations are illustrated for a dot made of three atoms. The results derived
here are also the starting point to include the effect of electron-electron and
electron-phonon interactions on the transport properties of quantum dot arrays.
Different derivations of the exact lattice Green's functions are discussed
Overlap effects on benzene transmission
The Hšuckel molecular-orbital method (with overlap S) is used to derive the S - modified version of the renormalization equations, which are then employed to introduce overlap into the para-, meta- and ortho-benzene dimersâ parameters. Invoking the Lippmann-Schwinger scattering theory enables the spectral energy transmission function T ( E) to be found for each of the benzene types. The effect of overlap on the behaviour of the various T(E) curves is, indeed, marked, even for low values of S, where all the curvesâ symmetries become permanently broken. As S increases, the graphs become more distorted and suffer displacements to lower energies. These results are so significant that they justify the inclusion of overlap in all T ( E) studies of benzene
Tensorial green-function theory of atomic-wire T-junction transmission
A tensorial Green-function treatment of the electronic transmission properties of an atomic wire T-junction is presented within the framework of the tight-binding approximation. The adoption of the tensorial formalism enables overlap effects to be included in a straightforward manner, without the need to resort to a change in the Hilbert space. The T-junction structure and the presence of overlap effects both give rise to antiresonances. Although those due to the former are located inside the energy band, the latter appear at the band edges. The transmission is seen to depend in different ways on the bond energy and the overlap between the attached atom and the wire