Nano-scale displacement sensing based on van der Waals interactions

We propose that a nano-scale displacement sensor with high resolution in weak-force systems can be realized based on vertically stacked two-dimensional (2D) atomic corrugated layer materials bound through van der Waals (vdW) interactions. Using first-principles calculations, we found that the electronic structures of bi-layer blue phosphorus (BLBP) vary appreciably with lateral and vertical interlayer displacements. The variation of the electronic structure is attributed to the change of the interlayer distance dz for both the lateral and vertical displacement. For lateral displacement, the change of dz is induced by atomic layer corrugation. Despite the different stacking configurations of BLBP, we find that the change of the indirect band gap is proportional to dz(-2). Furthermore, this dz(-2) dependence is found to be applicable to other graphene-like corrugated bi-layer materials such as MoS2. BLBP represents a large family of bi-layer 2D atomic corrugated materials for which the electronic structure is sensitive to the interlayer vertical and lateral displacement, and thus could be used for a nano-scale displacement sensor. This can be done by monitoring the tunable electronic structure using absorption spectroscopy. Because this type of sensor is established on atomic layers coupled through vdW interactions, it provides unique applications in the measurements of nano-scale displacement induced by tiny external forces.