Significant effect of stacking on the electronic and optical properties of few-layer black phosphorus

The effect of the number of stacking layers and the type of stacking on the electronic and optical properties of bilayer and trilayer black phosphorus are investigated by using first-principles calculations within the framework of density functional theory. We find that inclusion of many-body effects (i.e., electron-electron and electron-hole interactions) modifies strongly both the electronic and optical properties of black phosphorus. While trilayer black phosphorus with a particular stacking type is found to be a metal by using semilocal functionals, it is predicted to have an electronic band gap of 0.82 eV when many-body effects are taken into account within the ${G}_{0}{W}_{0}$ scheme. Though different stacking types result in similar energetics, the size of the band gap and the optical response of bilayer and trilayer phosphorene are very sensitive to the number of layers and the stacking type. Regardless of the number of layers and the type of stacking, bilayer and trilayer black phosphorus are direct band gap semiconductors whose band gaps vary within a range of 0.3 eV. Stacking arrangements that are different from the ground state structure in both bilayer and trilayer black phosphorus exhibit significant modified valence bands along the zigzag direction and result in larger hole effective masses. The optical gap of bilayer (trilayer) black phosphorus varies by 0.4 (0.6) eV when changing the stacking type. The calculated binding energy of the bound exciton hardly changes with the type of stacking and is found to be 0.44 (0.30) eV for bilayer (trilayer) phosphorous.