  Layered materials such as graphite and transition metal dichalcogenides have
extremely anisotropic mechanical properties owing to orders of magnitude
difference between in-plane and out-of-plane interatomic interaction strengths.
Although effects of mechanical perturbations on either intra- or inter-layer
interactions have been extensively investigated, mutual correlations between
them have rarely been addressed. Here we show that layered materials have an
inevitable coupling between in-plane uniaxial strain and interlayer shear.
Because of this, the uniaxial in-plane strain induces an anomalous splitting of
the degenerate interlayer shear phonon modes such that the split shear mode
along the tensile strain is not softened but hardened contrary to the case of
intralayer phonon modes. We confirm the effect by measuring Raman shifts of
shear modes of bilayer MoS2 under strain. Moreover, by analyzing the splitting,
we obtain an unexplored off-diagonal elastic constant, demonstrating that Raman
spectroscopy can determine almost all mechanical constants of layered
materials.
