Local deformation is a control knob to dynamically tune the electronic band structure of 2D semiconductors. This study demonstrates the local strain-dependent phonon properties of monolayer tungsten diselenide, which are investigated by using the scanning tunneling microscopy-based tip-enhanced Raman spectroscopy. The anomalous appearance and softening of the Raman-inactive out-of-plane A2'' (Γ) mode are first revealed, which exhibits equivalent behavior to other principal phonons of tungsten diselenide. Local strain calculations unveiled the linear proportionalities of A2'' (Γ) phonon nature on strain and it facilitates the derivation of Grüneisen parameter by experimental and theoretical approaches. Additionally, the origins of the anomalous appearance of the Raman-inactive A2'' (Γ) mode are clearly proved in both classical physics and quantum mechanics. Especially quantum mechanical calculations have precisely described strain-induced selection rule relaxation by polarizability changes. The first discovery provides a fundamental understanding of the strain-dependent phonon properties, as well as suggesting a new distinct strain indicator, A2'' (Γ) mode, for strain engineering.
