Using first-principles calculations, we study the dependence of the electronic and vibrational properties of multilayered ${\mathrm{PbI}}_2$ crystals on the number of layers and focus on the electronic-band structure and the Raman spectrum. Electronic-band structure calculations reveal that the direct or indirect semiconducting behavior of ${\mathrm{PbI}}_2$ is strongly influenced by the number of layers. We find that at 3L thickness there is a direct-to-indirect band gap transition (from bulk-to-monolayer). It is shown that in the Raman spectrum two prominent peaks, $A_{1g}$ and $E_g$, exhibit phonon hardening with an increasing number of layers due to the interlayer van der Waals interaction. Moreover, the Raman activity of the $A_{1g}$ mode significantly increases with an increasing number of layers due to the enhanced out-of-plane dielectric constant in the few-layer case. We further characterize rigid-layer vibrations of low-frequency interlayer shear (C) and breathing (LB) modes in few-layer ${\mathrm{PbI}}_2$. A reduced monoatomic (linear) chain model (LCM) provides a fairly accurate picture of the number of layers dependence of the low-frequency modes and it is shown also to be a powerful tool to study the interlayer coupling strength in layered ${\mathrm{PbI}}_2$.

• Received 6 June 2018
• Revised 16 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085431