  The encapsulation of few-layer transition metal dichalcogenides (TMDs) in
hexagonal boron nitride (h-BN) is known to improve significantly their optical
and electronic properties. However, it may be expected that the h-BN
encapsulation may affect also vibration properties of TMDs due to an atomically
flat surface of h-BN layers. In order to study its effect on interlayer
interactions in few-layer TMDs, we investigate low-energy Raman scattering
spectra of bi- and trilayer MoTe$_2$. Surprisingly, three breathing modes are
observed in the Raman spectra of the structures deposited on or encapsulated in
h-BN as compared to a single breathing mode for the flakes deposited on a
SiO$_2$/Si substrate. The shear mode is not affected by changing the MoTe$_2$
environment. The emerged structure of breathing modes is ascribed to the
apparent interaction between the MoTe$_2$ layer and the bottom h-BN flake. The
structure becomes visible due to a high-quality surface of the former flake.
Consequently, the observed triple structure of breathing modes originates from
the combination modes due to interlayer and layer-substrate interactions. Our
results confirm that the h-BN encapsulation affects substantially vibration
properties of layered materials.
