Peierls transition, ferroelectricity, and spin-singlet formation in monolayer VOI2

Using ab initio density functional theory and single-orbital Hubbard model calculations via the density matrix renormalization group method, we systematically studied the monolayer ${\mathrm{VOI}}_{2}$ with a $3{d}^{1}$ electronic configuration. Our phonon calculations indicate that the orthorhombic $Pmm2$ FE-II phase is the most likely ground state, involving a ferroelectric (FE) distortion along the $a$ axis and V-V dimerization along the $b$ axis. Specifically, the ``pseudo Jahn-Teller'' effect caused by the coupling between empty V (${d}_{xz/yz}$ and ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$) and O $2p$ states is proposed as the mechanism that stabilizes the FE distortion from the paraelectric phase. Moreover, the half-filled metallic ${d}_{xy}$ band displays a Peierls instability along the $b$ axis, inducing a V-V dimerization. We also found very short-range antiferromagnetic coupling along the V-V chain due to the formation of nearly decoupled spin singlets in the ground state.