Anomalous Phonon Softening with Inherent Strain in Wrinkled Monolayer WSe₂.

Abstract

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 <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msubsup><mi>A</mi> <mn>2</mn> <msup><mrow></mrow> <mrow><mo>'</mo> <mo>'</mo></mrow> </msup> </msubsup> <mrow><mo>(</mo> <mi>Γ</mi> <mo>)</mo></mrow> </mrow> <annotation>$A_2^{^{\prime\prime}}( \Gamma )$</annotation></semantics> </math> mode are first revealed, which exhibits equivalent behavior to other principal phonons of tungsten diselenide. Local strain calculations unveiled the linear proportionalities of <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msubsup><mi>A</mi> <mn>2</mn> <msup><mrow></mrow> <mrow><mo>'</mo> <mo>'</mo></mrow> </msup> </msubsup> <mrow><mo>(</mo> <mi>Γ</mi> <mo>)</mo></mrow> </mrow> <annotation>$A_2^{^{\prime\prime}}( \Gamma )$</annotation></semantics> </math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msubsup><mi>A</mi> <mn>2</mn> <msup><mrow></mrow> <mrow><mo>'</mo> <mo>'</mo></mrow> </msup> </msubsup> <mrow><mo>(</mo> <mi>Γ</mi> <mo>)</mo></mrow> </mrow> <annotation>$A_2^{^{\prime\prime}}( \Gamma )$</annotation></semantics> </math> 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, <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msubsup><mi>A</mi> <mn>2</mn> <msup><mrow></mrow> <mrow><mo>'</mo> <mo>'</mo></mrow> </msup> </msubsup> <mrow><mo>(</mo> <mi>Γ</mi> <mo>)</mo></mrow> </mrow> <annotation>$A_2^{^{\prime\prime}}( \Gamma )$</annotation></semantics> </math> mode, for strain engineering.