Absence of phonon softening across a charge density wave transition due to quantum fluctuations

Kagome metals have emerged as a frontier in condensed matter physics due to their potential to host exotic quantum states. Among these, CsV₃Sb₅ has attracted significant attention for the unusual coexistence of charge density wave (CDW) order and unconventional superconductivity, presenting an ideal system for exploring the emergent phenomena from the interplay of phonons, electronic fluctuations, and topological effects. The nature of CDW formation in CsV₃Sb₅ is unconventional and has sparked considerable debate. In this study, we examine the origin of the CDW state via ab initio finite-temperature simulations of the lattice dynamics. Through a comparative study of CsV₃Sb₅ and 2H-NbSe₂, we demonstrate that the experimental absence of phonon softening-a hallmark of conventional CDW transition-in CsV₃Sb₅ along with the presence of a weakly first-order transition, can be attributed to quantum zero-point atomic motion. This zero-point motion smears the free energy landscape of CDW, effectively stabilizing the pristine structure even below the CDW transition temperature. We argue that this surprising behavior could cause coexistence of pristine and CDW structures across the transition and lead to a weak first-order transition. Our predicted lattice dynamical behavior is supported by coherent phonon spectroscopy in single-crystalline CsV₃Sb₅. Our results provide crucial insights into the formation mechanism of CDW materials that exhibit little to no phonon softening, including cuprates, and highlight the surprising role of quantum effects in emergent properties of relatively heavy-element materials like CsV₃Sb₅.