Effective-mass theory for the anisotropic exciton in two-dimensional crystals: Application to phosphorene

Abstract

We present a theoretical study of the exciton binding energy for anisotropic two-dimensional crystals. We obtain analytical expressions from variational wave functions in different limits of the screening length to exciton size ratio and compare them with numerical solutions, both variational and exact. As an example, we apply these results to phosphorene, a monolayer of black phosphorous. Aided by density-functional-theory calculations for the evaluation of the two-dimensional polarizability, our analytical solution for the exciton binding energy gives a result which compares well with numerical ones and, in turn, with experimental values, as recently reported ; This work was supported by MINECO under Grants No. FIS2013-47328 and No. FIS2012-37549, by European Union structural funds and the Comunidad de Madrid Programs S2013/MIT-3007 and P2013/MIT-2850, and by Generalitat Valenciana under Grant No. PROMETEO/2012/011. E.P. also acknowledges the Ramón y Cajal Program