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