FINAL REPORT: Scalable Methods for Electronic Excitations and Optical Responses of Nanostructures: Mathematics to Algorithms to Observables

Work in nanoscience has increased substantially in recent years owing to its potential technological applications and to fundamental scientific interest. A driving force for this activity is to capitalize on new phenomena that occurs at the nanoscale. For example, the physical confinement of electronic states, i.e., quantum confinement, can dramatically alter the electronic and optical properties of matter. A prime example of this occurs for the optical properties of nanoscale crystals such as those composed of elemental silicon. Silicon in the bulk state is optically inactive due to the small size of the optical gap, which can only be accessed by “indirect” transitions. However, at the nanoscale, this material becomes optically active. The size of the optical gap is increased by confinement and the conservation of crystal momentum ceases to hold, resulting in the viability of indirect transitions. Our work associated with this grant has focused on developing new scalable algorithms for describing the electronic and optical properties of matter at the nanoscale such as nano structures of silicon and related semiconductor properties