Commensurate Stacking-Induced Ultrahigh Yet Discontinuous Bending Stiffness of the Double-Layer Black Phosphorus

Abstract

Black phosphorus (BP) has a considerable prospect in flexible electronics due to its atomic thickness and excellent photoelectric properties. Notably, their unique puckered surface makes flexible devices with highly adjustable bending performance possible. Here, a novel computational method for predicting the bending property of 2D materials is proposed based on molecular dynamics, focusing on the bending behavior of single- and double-layer BP. The results indicate that the bending stiffness of single-layer BP exhibits a significant chiral dependence. For double-layer BP, the bending stiffness varies from 6.35 to 54.77 eV, which depends on the stacking order and bending amplitude. The ultrahigh bending stiffness is about 10 ~ 13 times larger than that of single-layer BP, but it will undergo an abrupt reduction when the bending angle exceeds the critical value. The mechanism of the abrupt change is attributed to the interfacial structural transition from commensurability-induced self-locking to unlocking by analyzing the cooperative adjustment between the interlayer spacing, characteristic size and interlayer structures. This work reveals that the number of layers, stacking order and bending amplitude are vital factors affecting the bending stiffness of multi-layer 2D materials. Thus, 2D structural design provides an effective strategy for preparing on-demand flexible devices.

Keywords: black phosphorus, bending stiffness, commensurate stacking, interlayer lattice structure, Molecular dynamics