Anomalous Phonon Softening with Inherent Strain in Wrinkled Monolayer WSe₂

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 $A_2^{{}^{\text{'}\text{'}}}\left(\Gamma \right)$ mode are first revealed, which exhibits equivalent behavior to other principal phonons of tungsten diselenide. Local strain calculations unveiled the linear proportionalities of $A_2^{{}^{\text{'}\text{'}}}\left(\Gamma \right)$ 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 $A_2^{{}^{\text{'}\text{'}}}\left(\Gamma \right)$ 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, $A_2^{{}^{\text{'}\text{'}}}\left(\Gamma \right)$ mode, for strain engineering.