Physical Fingerprints of the 2O-tαP Phase in Phosphorene Stacking

The 2O-tαP phase is a bilayer phosphorene stacking twisted by ∼70.5° standing out from all the potential candidates predicted by our previous work. Here, by linear response theory, we directly verified that the 2O-tαP phase preserves the intrinsic features of phonon spectrum of the existing AB phase, reflecting a stable thermodynamic behavior. Then we provided three distinct fingerprints to help finding this new phase: upon comparison to the existing shifting bilayer phosphorene, the in-plane elastic constants showed a much weaker anisotropic response, providing a characteristic mechanical criterion; the calculated Raman spectrum revealed for the low frequency rang the layer-breathing mode and the out-of-plane twisted mode, L-A¹ and L-A², both of which together stabilize the twisted structure; in particular, the simulated scanning tunneling microscope image presented recognizable cross stripes, which should withstand an examination of exfoliated bilayer and few-layer black phosphorus.