Electronic dispersions of a stable twisted bilayer phosphorene in 2O-tαP phase

Abstract

It is reported for the electronic properties of an in-plane twisted bilayer phosphorene, known as the 2O-tαP phase, and the only dynamically stable phase beyond the AB stacking. This was achieved using first-principles calculations, a generalized empirical tight-binding model inclusive of electric field effects, and a two-parameter low energy effective model, the latter two providing an efficient scheme for nanoelectronics related applications. The tight-binding model reproduces a global fit to the first-principles dispersion, and the low energy model provides more accurate near-gap bands. Both are orders-of-magnitude faster and less memory-intensive than performing first-principles calculations. The twisted 2O-tαP structure possesses a direct bandgap of 1.27 eV, larger than that of the shifted AB structure (1.03 eV). The hole and electron polar effective mass anisotropy ratios are 27.34 and 1.95, respectively. An important observation is that the layer twisting results in the removal of Dirac cones as a reflection of a different band topology compared to the AB one, while the twofold degeneracy at the Brillouin zone boundary and the symmetry of the energy surface are both broken by an external vertical electric field. With an increasing electric field strength, a decreasing bandgap and an increasing energy difference between the valence band maximum and the twisted band point are both predicted by the tight-binding model and the low energy model.