Quantum Networks & Faster nanowires

Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires connected at vertices. In this paper, we discuss the solutions of the Schrodinger equation on such graphs, which have been named "quantum networks". Such solutions are needed for finding the energy spectrum of single electrons on such finite systems or for finding the transmission of electrons between leads which connect such systems to reservoirs. Specifically, we compare two common approaches. In the "continuum" approach, one solves the one-dimensional Schrodinger equation on each continuous wire and then uses the Neumann-Kirchoff-de Gennes matching conditions at the vertices. Alternatively, one replaces each wire by a finite number of "atoms" and then uses the tight binding model for the solution. Here, we show that these approaches cannot generally give the same results, except for special energies, unless the lattice constant of the tight binding model tends to zero. Even in the limit of the vanishing lattice constant, the two approaches coincide only if the tight binding parameters obey very special relations. The different consequences of the two approaches are then demonstrated via the example of a T-shaped scatterer.

Aharony et al: J Phys Chem B. 2008 Nov 24.



Electricity moves through nanowires very differently from ordinary electrical wires. "If you add electrons to a typical metal wire, a domino effect moves them along the wire until they dump out the other end," says Chidsey. The electrons in metal wire move at a constant speed as they bump each other across the wire. Cut the length of a metal wire in half and it will take half as long for electrons to pass through it.

But organic nanowires don't conduct electricity that way. The rate of speed increases exponentially as the wires get shorter. For example, a 3-nanometer wire of OPV would conduct 950 times faster than a wire that's twice as long. That's because instead of bumping each other across the wire domino style, electrons "tunnel" through nanowires. When they tunnel, electrons bypass barriers they normally would not be able to climb without violating the law of conservation of energy. The chance they'll make it through to the other side drops exponentially with distance.

The OPV nanowire allows tunneling to occur relatively easily. In computer chips, tunneling is mostly a bad thing, Chidsey says: When electrons tunnel through a thin insulator around a circuit, they may cause it to short out. "I'm interested in seeing if we can understand and get control over tunneling through molecules," he says. And if he succeeds, tunneling may get a better reputation in electronics, as it may be harnessed for moving electrons between nanostructures.

http://www.stanford.edu/dept/news/pr/01/nanowire314.html