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We report experimental evidence of charge density wave (CDW) transition in monolayer 1T-VTe$_2$ film. 4$times$4 reconstruction peaks are observed by low energy electron diffraction below the transition temperature $T_{CDW}$ = 186 K. Angle-resolved ph otoemission spectroscopy measurements reveal arc-like pockets with anisotropic CDW gaps up to 50 meV. The anisotropic CDW gap is attributed to the imperfect nesting of the CDW wave vector, and first-principles calculations reveal phonon softening at the same vector, suggesting the important roles of Fermi surface nesting and electron-phonon interaction in the CDW mechanism.
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