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A full gap above the Fermi level: the charge density wave of monolayer VS2

In the standard model of charge density wave (CDW) transitions, the displacement along a single phonon mode lowers the total electronic energy by creating a gap at the Fermi level, making the CDW a metal--insulator transition. Here, using scanning tunneling microscopy and spectroscopy and ab initio calculations, we show that VS$_2$ realizes a CDW which stands out of this standard model. There is a full CDW gap residing in the unoccupied states of monolayer VS$_2$. At the Fermi level, the CDW induces a topological metal-metal (Lifshitz) transition. Non-linear coupling of transverse and longitudinal phonons is essential for the formation of the CDW and the full gap above the Fermi level. Additionally, x-ray magnetic circular dichroism reveals the absence of net magnetization in this phase, pointing to coexisting charge and spin density waves in the ground state.