Insight into the stacking effect on shifted patterns of bilayer phosphorene: a comprehensive first-principles study

It is crucial to deeply understand how the interlayer interaction acts on controlling the structural and electronic properties of shifted patterns of bilayer phosphorene. A comprehensive first-principles study on the bilayer phosphorene through relative translation along different directions has revealed that there is a direct correlation between the potential energy surface and the interlayer equilibrium distance. The shorter the interlayer distance, the lower the potential energy surface. The shifted patterns with the most stable state, the metastable state, and the transition state (with energy barrier of ∼1.3 meV/atom) were found associated with the AB, the Aδ, and the TS stacking configurations, respectively. The high energy barriers, on the other hand, are ∼9.3 meV/atom at the AA stacking configuration along the zigzag pathway, ∼5.3 meV/atom at the AB' stacking configuration along the armchair pathway, and ∼11.2 meV/atom at the AA' stacking configuration along the diagonal pathway, respectively. The character of electronic bandgap with respect to the shifting shows an anisotropic behavior (with the value of 0.69-1.22 eV). A transition from the indirect to the direct bandgap occurs under the shifting, implying a tunable bandgap by stacking engineering. Furthermore, the orbital hybridization at the interfacial region induces a redistribution of the net charge (∼0.002-0.011e) associated with the relative shifting between layers, leading to a strong polarization with stripe-like electron depletion near the lone pairs and accumulation in the middle of the interfacial region. It is expected that such interesting findings will provide a fundamental reference to deeply understand and analyze the complex local structural and electronic properties of twisted bilayer phosphorene and will make the shifted patterns of bilayer phosphorene promising for nanoelectronics as versatile shiftronics materials.