Pseudo-Jahn-Teller Distortion in Two-Dimensional Phosphorus: Origin of Black and Blue Phases of Phosphorene and Band Gap Modulation by Molecular Charge Transfer

Phosphorene (Pn) is stabilized as a layered material like graphite, yet it possess a natural direct band gap (E-g = 2.0 eV). Interestingly, unlike graphene, Pn exhibits a much richer phase diagram which includes distorted forms like the stapler-clip (black Pn, alpha form) and chairlike (blue Pn, beta form) structures. The existence of these phases is attributed to pseudo-Jahn-Teller (PJT) instability of planar hexagonal P-6(6-) rings. In both cases, the condition for vibronic instability of the planar P-6(6-) rings is satisfied. Doping with electron donors like tetrathiafulvalene and tetraamino-tetrathiafulvalene and electron acceptors like tetracyanoquinodimethane and tetracyanoethylene convert blue Pn into N-type and black Pn into efficient P-type semiconductors, respectively. Interestingly, pristine blue Pn, an indirect gap semiconductor, gets converted into a direct gap semiconductor on electron or hole doping. Because of comparatively smaller undulation in blue Pn (with respect to black Pn), the van der Waals interactions between the dopants and blue Pn is stronger. PJT distortions for two-dimensional phosphorus provides a unified understanding of structural features and chemical reactivity in its different phases.