Unraveling the not-so-large trion binding energy in monolayer black phosphorus

Black phosphorus (bP) is a promising two-dimensional (2D) material for opto-electronic applications. Strongly bound excitons with binding energies up to 0.3 eV and remarkably large trion binding energies up to 100 meV have been observed for supported monolayer bP. Surprisingly, this trion binding energy is significantly larger than those found in other 2D materials (e.g. about 30 meV in transition metal dichalcogenides). This has previously been ascribed to the quasi-1D nature of bP. In this work we show, using first principles calculations, that the trion binding energy of bP is indeed large (80 meV) when referenced to the lowest bright exciton but only 30 meV when its energy is measured relative to the lowest dark exciton. Our analysis thus shows that the trion binding energy in bP is not larger than in other 2D materials, and the previous conclusions have to be understood incorporating the large splitting between the dark and bright excitons in bP. We also explore the effect of substrate and in-plane strain of the exciton and trion binding energies and show that these effects do not change the main conclusions. Our results correct the misconception that trion binding energies in monolayer bP are particularly large due to its quasi-1D structure and contribute to the establishment of more a detailed understanding of optical properties of atomically thin semiconductors.