Scaleability of dielectric susceptibility $\epsilon_{zz}$ with the number of layers and additivity of ferroelectric polarization in van der Waals semiconductors

We study the dielectric response of few layered crystals of various transition metal dichalcogenides (TMDs) and hexagonal Boron Nitride (hBN). We showed that the out-of-plane polarizability of a multilayer crystal (which characterizes response to the external displacement field) scales linearly with the number of layers, $\alpha_{zz}^{NL} =N \alpha_{zz}^{1L}$, independently of the stacking configuration in the film. We also established additivity of ferroelectric polarizations of consecutive interfaces in case when such interfaces have broken inversion symmetry. Then we used the obtained data of monolayer $\alpha_{zz}^{1L}$ to calculate the values of the dielectric susceptibilities for semiconductor TMDs and hBN bulk crystals.