Nondestructive picosecond ultrasonic probing of intralayer and van der Waals interlayer bonding in α- and β-In₂Se₃

The interplay between the strong intralayer covalent-ionic bonds and the weak interlayer van der Waals (vdW) forces between the neighboring layers of vdW crystals give rise to unique physical and chemical properties. Here, we study the intralayer and interlayer bonding in α and β polytypes of In₂Se₃, a vdW material with potential applications in advanced electronic and optical devices. We conduct picosecond ultrasonic experiments to probe the sound velocity in the direction perpendicular to the vdW layers. The measured sound velocities are different in α- and β-In₂Se₃, suggesting a significant difference in their elastic properties. We use density functional theory and an effective spring model to calculate the elastic stiffness of the layer and vdW gap in α- and β-In₂Se₃. The calculated elastic moduli show good agreement with experimental values and reveal the dominant contribution of interlayer atomic bonding to the different elastic properties of the two polytypes. Our findings show the power of picosecond ultrasonics for probing the fundamental elastic properties of vdW materials; also, our data and analysis provide a reliable description of the intra- and inter-layer forces in complex crystal structures, such as the polytype phases of In₂Se₃.