Abnormal scaling of excitons in phosphorene quantum dots

Abstract

Excitonic states of a many-electron system in phosphorene quantum dots (PQDs) are investigated theoretically by using a configuration interaction approach. For a triangular PQD in various dielectric environments, its exciton is found to obey two distinct scaling rules. When there is a strong screening effect present in the nanodot, the exciton binding energy (Δ_ex) is shown to be around −150 meV as the long-range Coulomb interactions are totally suppressed and it increases to about 100 meV when the effective dielectric constant (ε_r) decreases to 12.5. Over this range of ε_r, Δ_ex is found to be well fitted into a quadratic form of ε_r⁻¹, which scales neither linearly with ε_r⁻² like the case of bulk three-dimensional semiconductors nor linearly with ε_r⁻¹ like the case previously reported for graphene nanostructures. When ε_r is reduced below 10.0, however, Δ_ex is shown to exhibit a perfect linear relationship with ε_r⁻¹, which behaves just like that of a two-dimensional graphene sheet. On the other hand, with the reduced ε_r, the quasiparticle gap is found to decrease instead of increasing like in most of the semiconductor nanostructures. As a result, it is revealed that the relationship of Δ_ex with the quasi-particle gap deviates largely from the linear one previously reported for graphene and many other two-dimensional materials.