The role of Coulomb correlation in charge density wave of CuTe

A quasi one-dimensional layered material, CuTe undergoes a charge density wave (CDW) transition in Te chains with a modulation vector of $q_{CDW}=(0.4, 0.0, 0.5)$. Despite the clear experimental evidence for the CDW, the theoretical understanding especially the role of the electron-electron correlation in the CDW has not been fully explored. Here, using first principles calculations, we demonstrate the correlation effect of Cu is critical to stabilize the 5$\times$1$\times$2 modulation of Te chains. We find that the phonon calculation with the strong Coulomb correlation exhibits the imaginary phonon frequency so-called phonon soft mode at $q_{ph0}=(0.4, 0.0, 0.5)$ indicating the structural instability. The corresponding lattice distortion of the soft mode agrees well with the experimental modulation. These results demonstrate that the CDW transition in CuTe originates from the interplay of the Coulomb correlation and electron-phonon interaction.