- Consider A 2 Dimensional Electron System With A Simple Square Lattice Lattice Constant A 1 Atom Per Lattice Point An 1 (43.76 KiB) Viewed 37 times
Consider a 2 dimensional electron system, with a simple square lattice (lattice constant a), 1 atom per lattice point and 2 electrons per atom. (a) In a free electron model, what fraction of the electrons will be in the first Bril- louin Zone and what fraction in the second? (b) Argue why this material will be a metal in the nearly free electron approximation. (Argue either from an energy contour plot, or by plotting E(k) versus k for k parallel to (n/a, 0) and (T/a, 7/a), or from both. No messy calculations are needed to answer this question!) (c) Suppose for the sake of simplicity that the energy gap along the BZ boundary is equal Eg. (In real materials, E, depends on position on the zone boundary.). How large E, have to be (a rough estimate) for this material to be an insulator instead of a metal?