Poisson's Ratio of Layered Two-dimensional Crystals

We have investigated the elastic properties of multilayered graphene as well as h-BN and MoS$_2$ using a first-principles approach with up-to-date nonlocal exchange-correlation energy functional. Our analysis shows that the Poisson's ratios of multilayered graphene, h-BN and MoS$_2$ along out-of-plane direction are negative, near zero and positive, respectively, spanning all possibilities for sign of the ratios. While the in-plane Poisson's ratios are positive regardless of their disparate electronic and structural properties, the characteristic interlayer interactions as well as atomic stacking structures are shown to determine the sign of their out-of-plane ratios, highlighting their intertwined nature between elastic and electronic properties.