  We present vibrational properties of Franckeite, which is a naturally
occurring van der Waals heterostructure consisting of two different
semiconducting layers. Franckeite is a complex layered crystal composed of
alternating SnS$_2$ like pseudohexagonal and PbS-like pseudotetragonal layers
stacked on top of each other, providing a unique platform to study vibrational
properties and thermal transport across layers with mass density and phonon
mismatches. By using micro-Raman spectroscopy and first-principles Raman
simulations, we found that the PbS-like pseudotetragonal structure is mostly
composed of Pb$_3$SbS$_4$. We also discovered several low-frequency Raman modes
that originate from the intralayer vibrations of the pseudotetragonal layer.
Using density functional theory, we determined all vibrational patterns of
Franckeite, whose signatures are observed in the Raman spectrum. By studying
temperature dependent Raman spectroscopy (300 K - 500 K), we have found
different temperature coefficients for both pseudotetragonal and
pseudohexagonal layers. We believe that our study will help understand the
vibration modes of its complex heterostructure and the thermal properties at
the nanoscale.
