Electronic and Vibrational Properties of PbI 2 : From Bulk to Monolayer
Using first-principles calculations, we study the dependence of the electronic and vibrational properties of multi-layered 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 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 increasing number of layers due to the inter-layer van der Waals interaction. Moreover, the Raman activity of the A 1g mode significantly increases with 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 inter-layer shear (C) and breathing (LB) modes in few-layer PbI 2 . A reduced mono-atomic (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 inter-layer coupling strength in layered PbI 2 .