My work has concentrated on two aspects of quantum wire systems. The first is to adapt state-of-the-art atomic scattering theory to electronic devices. The second is to apply this theory to a number of interesting devices.
Scattering theory has been highly refined by atomic and molecular theorists who have to deal with manybody problems. Often we in condensed matter are unaware of algorithms that improve the speed and accuracy of calculations. I have collaborated with Michael Morrison to apply R-matrix theory to two dimensional devices. R-matrix theory is computationally simple and efficient and holds great promise for molecular wire systems.
Device applications include calculating the negative bend resistance seen in InSb quantum wires (grown here at OU), and calculating the cooling possible in non-equilibrium systems we have dubbed "electron refrigerators." The latter is depicted below on the left: electrons are injected in the first two subbands and encounter a "T-junction." We hypothesize that the upper subband electrons, because they have more transverse momentum, will scatter more easily down the sidearms. This is born out by the forward transmission coefficients plotted below on the right. Note that the higher the band number, the higher the chance to go down the sidearm and the lower the chance to scatter foward. We can use this to get cooling in the subpopulation of forward scattered electrons.