Wrinkle Effect in Monolayer Phosphorene

Two-dimensional materials with tunable wrinkled structures opening up a new avenue to modulate their electronic and optoelectronic properties. However, the formation mechanisms of wrinkles and their influences on the band structures and associated properties remain relatively uncharacterized. In this work, we investigate the energy funneling and flexoelectricity induced by the wrinkle geometrical effect in black and blue phosphorene through the atomic-bond-relaxation approach, Marcus theory, and first-principles calculations. By comparing the results between the two materials, we find that the wrinkled black phosphorene exhibits anisotropic inverse energy funneling in different directions of wrinkles, whereas the wrinkled blue phosphorene exhibits energy funneling. Importantly, energy funneling (inverse energy funneling) results in the accumulation of excitons at the top (valley) regions of the wrinkles, and the accumulation rate increases with decreasing wrinkle wavelength. In addition, symmetry breaking in the wrinkles leads to a strong flexoelectric effect, and the flexoelectricity is dependent on the type and chirality of phosphorene. These findings could enable the creation of a new paradigm for enhancing the optoelectronic performance of two-dimensional materials.