Electron-phonon driven charge density wave in CuTe
Marco Campetella, Giovanni Marini, Jianqiang Sky Zhou, Matteo Calandra
Abstract
The compound CuTe (vulcanite) undergoes a quasi-one-dimensional charge density wave (CDW) at $T<{T}_{\mathrm{CDW}}=335$ K with a $5\ifmmode\times\else\texttimes\fi{}1\ifmmode\times\else\texttimes\fi{}2$ periodicity. The mechanism at its origin is debated. Several theoretical works claimed that semilocal functionals are unable to describe its occurrence and ascribed its formation only to strong electron-electron interaction. Moreover, the possible role of quantum anharmonicity has not been addressed. Here, by performing quantum-anharmonic calculations, we show that semilocal functionals correctly describe the occurrence of a CDW in CuTe if ultradense electron-momentum grids allowing for small electronic temperatures are used. The distortion is driven by the perfect nesting among one-dimensional Fermi surface sheets extending in the ${k}_{y}$ direction. Quantum anharmonic effects are important and tend to suppress both the distortion and ${T}_{\mathrm{CDW}}$. The quantum anharmonic structural minimization of the CDW phase in the generalized gradient approximation leads, however, to distorted Te-Te bond lengths in the low temperature phase that are $21%$ of the experimental ones at $T=20$ K. This suggests that, even if the electron-electron interaction is not crucial for the mechanism of CDW formation, it is relevant to accurately describe the structural data for the low-$T$ phase. We assess the effect of electron-electron interaction on the CDW by using the $\text{DFT}+U+V$ approximation with parameters calculated from first principles. We find that electron-electron interaction enhances the Te-Te distortion, ${T}_{\mathrm{CDW}}$, and the total energy gain by the distortion.