Three-dimensional charge density wave observed by angle-resolved photoemission spectroscopy in 1T −VSe2

We apply high-resolution angle-resolved photoemission spectroscopy to explore the layered transition-metal dichalcogenide $1T\ensuremath{-}{\mathrm{VSe}}₂$ with various photon energies to investigate the three-dimensional (3D) charge-density wave (CDW) transition. Here, we provide quite comprehensive evidence of 3D Fermi surface nesting in $1T\ensuremath{-}{\mathrm{VSe}}₂$. The observed Fermi surface (FS) largely overlaps with the in-plane nesting vector reported by the electron-diffraction results. Comparing the CDW gaps below and above ${T}_c$, we find that the gaps open along the ellipsoidal FS around the $\overline{M}$ point, in agreement with the in-plane nesting vector. With varying the photon energy, a warping of FS and the nesting condition along ${k}_z$ are observed. We further observe the gap variation along the ${k}_z$ direction consistent with the out-of-plane nesting conditions. Although it was believed to be a layered two-dimensional material, the satisfaction of the 3D nesting condition of the FS and the variation of gap distribution suggest a 3D character of CDW in $1T\ensuremath{-}{\mathrm{VSe}}₂$. Meanwhile, a larger value of $2\mathrm{\ensuremath{\Delta}}/{k}_B{T}_c$ = 14.76 suggests CDW in $1T\ensuremath{-}{\mathrm{VSe}}₂$ beyond the weak-coupling region, the nesting condition and the gap correspondence implies a combined effort in the formation of CDW in this material.