Current Flow In 2-Dimensional Quantum Systems

Abstract

We use the method of non-equilibrium Green’s Functions to investigate the current flow in 2-dimensional conductors. We found that by varying the Fermi energy of the system, three different classes of current density profiles could be achieved. In addition to the effects of the Fermi energy of the system, we looked at the effects of mono- and di- vacancies on the resulting current flow. We found that the effects of a mono-vacany on each of the regimes of the Fermi energy varied between the regimes and was dependent on the location of the vacancy within each regime. When two vacancies were introduced into the system, the location effects seen in the mono-vacancy was still important, but the current was also dependent on the relative locations of the two vacancies. In both of these cases we saw current branching in all three regimes but we saw back-flow and vorticies in the low-band and middle-band regimes.