Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.
Pittalis, S., Raesaenen, E., Helbig, N., & Gross, E. K. U. (2007). Exchange-energy functionals for finite two-dimensional systems. Physical review. B, Condensed matter and materials physics, 76(23). https://doi.org/10.1103/PhysRevB.76.235314 (Original work published 2007)