Abstract by Nicolas Ducharme
Physics and Astronomy
Solid-state calculations in the irreducible Brillouin zone
Solutions to Schrodinger’s equation are essential to understanding the behavior of particles. In the case of many interacting particles arranged with periodic structure, Schrodinger’s equation predicts multiple values of energy for each momentum, as well as multiple values of momentum for each energy. The set of all unique wavevectors is known as the Brillouin zone. Analyzing the solution to Schrodinger’s equation for all wavevectors within the Brillouin zone thus describes all possible values of energy and momentum for the system. Therefore, methods for calculating the Brillouin zone are important in determining the properties of materials. By discarding regions of the Brillouin zone that are invariant under the symmetries of the system, the irreducible Brillouin zone can be calculated thereby reducing the region of integration and potentially discarding difficult-to-integrate regions.