  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 .
