Origin of the multiple charge density wave order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>VSe</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>
Jianguo Si, W. J. Lu, Hua Wu, Hongyan Lv, Xin Liang, Quanjun Li, Young Sun
Abstract
Transition-metal dichalcogenide $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$ experimentally exhibits multiple charge density wave (CDW) orders, but its origin is still under debate. Using first-principles calculations, we investigate the origin of CDW orders in $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$ and clarify the ground state of CDW in the freestanding monolayer. Our results show that both Fermi-surface nesting and electron-phonon coupling account for the $4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}3$ CDW superstructure in bulk $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$, while the momentum-dependent electron-phonon coupling-induced $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ CDW superstructure is most stable in the freestanding monolayer $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$. For monolayer $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$, the substrate-induced compressive strain can turn the ground state into the $4\ifmmode\times\else\texttimes\fi{}4$ CDW superstructure, while tensile strain preserves the $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ superstructure. Our results demonstrate the origin of the CDW orders in $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$ and shed light on the experimental observation of multiple CDW orders in monolayer $1T\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$.