Charge order from structured coupling in VSe\(_2\)

Abstract

Charge order is ubiquitous in the phase diagrams of correlated materials. It is customarily described in the weak-coupling limit, where the electron-phonon coupling is implicitly assumed to be featureless. Detailed comparison between the resulting theoretical predictions and modern, high-resolution experimental data, however, regularly yields paradoxical results. As a best-case scenario for the weak-coupling approach, we consider \(1T\)-VSe\(_2\), whose charge density wave (CDW) phase has a temperature-dependent, three-dimensional wave vector. We show that the electronic response in the weak-coupling limit cannot explain the observed thermal evolution, whereas consideration of a structured, momentum-dependent electron-phonon coupling does reproduce the measured result. The temperature dependence of the structured susceptibility moreover clarifies the apparent transition between two consecutive CDW phases observed in x-ray diffraction experiments, and suggests that a particle-hole asymmetry in the CDW gap results in its apparent absence in spectroscopic experiments. These results agree with recent findings in more strongly coupled compounds, and showcase both the use and the need of a structured coupling to obtain quantitative agreement with experiments in materials that would traditionally be considered unconventional.