Strong elastic coupling: Out-of-plane strain, negative Poisson's ratio, and linear bandgap tunability

Strain engineering is a promising strategy for tailoring the properties of two-dimensional (2D) materials. Despite the challenge of interlayer cleavage due to weak van der Waals interactions, by using in situ transmission electron microscopy, we demonstrate that large uniaxial tensile strain can be applied to black phosphorus (BP) not only along the zigzag (ZZ) and armchair (AC) directions but also in the out-of-plane (OP) direction. Notably, the maximum tensile strain along the OP direction reaches 5.0%, comparable to that along ZZ and AC directions. Moreover, a negative Poisson's ratio is directly observed between OP/AC and AC/OP directions, indicating strong elastic coupling originating from interlayer-intralayer electron redistribution under tensile strain. Interestingly, different from tensile strain along ZZ or AC, the bandgap of BP is linearly tunable under OP tensile strain. This work underscores OP tensile strain offering avenues for tuning electronic, optical, and magnetic properties of 2D materials and potential applications in strain electronics and flexible electronics.