Two-probe theory of scanning tunneling microscopy of single molecules: Zn(II)-etioporphyrin on alumina

We explore theoretically the scanning tunneling microscopy of single molecules on substrates using a framework of two local probes. This framework is appropriate for studying electron flow in tip/molecule/substrate systems where a thin insulating layer between the molecule and a conducting substrate transmits electrons non-uniformly and thus confines electron transmission between the molecule and substrate laterally to a nanoscale region significantly smaller in size than the molecule. The tip-molecule coupling and molecule-substrate coupling are treated on the same footing, as local probes to the molecule, with electron flow modelled using the Lippmann-Schwinger Green function scattering technique. STM images are simulated for various positions of the stationary (substrate) probe below a Zn(II)-etioporphyrin I molecule. We find that these images have a strong dependence on the substrate probe position, indicating that electron flow can depend strongly on both tip position and the location of the dominant molecule-substrate coupling. Differences in the STM images are explained in terms of the molecular orbitals that mediate electron flow in each case. Recent experimental results, showing STM topographs of Zn(II)-etioporphyrin I on alumina/NiAl(110) to be strongly dependent on which individual molecule on the substrate is being probed, are explained using this model. A further experimental test of the model is also proposed.Comment: Physical Review B, in pres

Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

Optical properties of tungsten thin films perforated with a bidimensional array of subwavelength holes

We present a theorical investigation of the optical transmission of a dielectric grating carved in a tungsten layer. For appropriate wavelengths tungsten shows indeed a dielectric behaviour. Our numerical simulations leads to theoretical results similar to those found with metallic systems studied in earlier works. The interpretation of our results rests on the idea that the transmission is correlated with the resonant response of eigenmodes coupled to evanescent diffraction orders.Comment: 4 pages, 3 figure