Theoretical exploration of third-order nonlinear optical properties of black phosphorus quantum dots doped with alkali and alkaline-earth metal atoms

Abstract

The electrical properties and nonlinear optical (NLO) properties of black phosphorus quantum dots (BPQDs) upon doping of alkali and alkaline-earth metal atoms, M@BPQDs (M = Li, Na, K, Be, Mg, and Ca), were systematically investigated based on density functional theory (DFT) method. The results showed that the introduction of metal atoms M could efficiently narrow the wide gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the pristine BPQDs in the range of 2.254–3.098 eV. More importantly, the metal atom M doping can remarkably enhance the second hyperpolarizability (γ0) of BPQDs, due to electron transfer from M to BPQDs. M@BPQDs possess large second hyperpolarizabilities (γ0) in the range of 0.81 × 10−33–3.94 × 10−33 esu, where the alkali-doped complexes are much superior to the alkaline-earth-doped complexes. Furthermore, doping heavier K atom on the large-sized BPQDs can obtain the largest γ0 value of 3.94 × 10−33 esu, which can be understood by its large amplitude distribution of second hyperpolarizability density. Configuration interaction singles (CIS) calculations were performed to get crucial excited states to account for the large γ0 values. The second hyperpolarizability trend estimated from the two-level formula and DFT calculations correlates nicely. These metal-doped complexes have the deep-ultraviolet (deep-UV) transparent region at wavelength ≤ 200 nm, and hence are new deep-UV NLO molecules. These striking results designate such doped BPQDs as excellent candidates for their potential applications in optical devices.