Using density functional theory-based first-principles calculations, we investigate the stacking order dependence of the electronic and vibrational properties of ${\mathrm{HfS}}_2-\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ heterobilayer structures. It is shown that while the different stacking types exhibit similar electronic and optical properties, they are distinguishable from each other in terms of their vibrational properties. Our findings on the vibrational properties are the following: (i) from the interlayer shear (SM) and layer breathing (LBM) modes we are able to deduce the ${\mathrm{AB}}^{\prime }$ stacking order, (ii) in addition, the ${\mathrm{AB}}^{\prime }$ stacking type can also be identified via the phonon softening of $E_g^{\text{I}}$ and $A_g^{\text{III}}$ modes which harden in the other two stacking types, and (iii) importantly, the ultrahigh frequency regime possesses distinctive properties from which we can distinguish between all stacking types. Moreover, the differences in optical and vibrational properties of various stacking types are driven by two physical effects, induced biaxial strain on the layers and the layer-layer interaction. Our results reveal that with both the phonon frequencies and corresponding activities, the Raman spectrum possesses distinctive properties for monitoring the stacking type in novel vertical heterostructures constructed by alkaline-earth-metal hydroxides.

• Received 18 January 2019
• Revised 27 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.205405