Evolution of electronic structure of few-layer phosphorene from angle-resolved photoemission spectroscopy of black phosphorous

A complete set of tight-binding parameters for the description of the quasiparticle dispersion relations of black phosphorous (BP) and N-layer phosphorene with N=1⋯∞ is presented. The parameters, which describe valence and conduction bands, are fit to angle-resolved photoemission spectroscopy (ARPES) data of pristine and lithium doped BP. We show that zone-folding of the experimental three-dimensional electronic band structure of BP is a simple and intuitive method to obtain the layer-dependent two-dimensional electronic structure of few-layer phosphorene. Zone folding yields the band gap of N-layer phosphorene in excellent quantitative agreement to experiments and ab initio calculations. A combined analysis of optical absorption and ARPES spectra of pristine and doped BP is used to estimate a value for the exciton binding energy of BP.