Role of Coulomb correlations in the 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 qCDW=(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 that the correlation effect of Cu is critical to stabilize the 5×1×2 modulation of Te chains. We find that the phonon calculation with the strong Coulomb correlation exhibits the imaginary phonon frequency, i.e., the so-called phonon soft mode, at qph0=(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.