Electron-phonon driven charge density wave in CuTe

TL;DR

This study demonstrates that semilocal functionals can accurately describe the charge density wave in CuTe when quantum anharmonic effects and dense electron momentum grids are considered, highlighting the role of Fermi surface nesting.

Contribution

It shows that quantum anharmonic calculations combined with semilocal functionals can explain the CDW in CuTe without invoking strong electron-electron interactions.

Findings

Quantum anharmonic effects suppress CDW distortion and transition temperature.

Fermi surface nesting drives the CDW distortion in CuTe.

Correlation effects enhance structural distortion and transition temperature.

Abstract

The compound CuTe (vulcanite) undergoes a quasi one dimensional charge density wave (CDW) at $T< T_{\mathrm{CDW}}=335$ K with a $5\times1\times2$ 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 1D 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 correlation on the CDW by using the DFT+U+V approximation with parameters calculated from first principles. We find that correlation enhances the Te-Te distortion, T$_{CDW}$ and the total energy gain by the distortion.