Layer-dependent exciton polarizability and the brightening of dark excitons in few-layer black phosphorus.

The evolution of excitons from 2D to 3D is of great importance in photo-physics, yet the layer-dependent exciton polarizability hasn't been investigated in 2D semiconductors. Here, we determine the exciton polarizabilities for 3- to 11-layer black phosphorus-a direct bandgap semiconductor regardless of the thickness-through frequency-resolved photocurrent measurements on dual-gate devices and unveil the carrier screening effect in relatively thicker samples. By taking advantage of the broadband photocurrent spectra, we are also able to reveal the exciton response for higher-index subbands under the gate electrical field. Surprisingly, dark excitons are brightened with intensity even stronger than the allowed transitions above certain electrical field. Our study not only sheds light on the exciton evolution with sample thickness, but also paves a way for optoelectronic applications of few-layer BP in modulators, tunable photodetectors, emitters and lasers.