Quasiparticle band structure and tight-binding model for single- and   bilayer black phosphorus
  By performing \emph{ab initio} calculations for one- to four-layer black phosphorus within the $GW$ approximation, we obtain a significant difference in the band gap ($\sim$1.5 eV), which is in line with recent experimental data. The results are analyzed in terms of the constructed four-band tight-binding model, which gives accurate descriptions of the mono- and bilayer band structure near the band gap, and reveal an important role of the interlayer hoppings, which are largely responsible for the obtained gap difference. 
Alexander N. Rudenko and Mikhail I. Katsnelson
cond-mat.mtrl-sci cond-mat.mes-hall cond-mat.str-el