Origin of competing charge density waves in kagome metal ScV_6Sn_6

Understanding competing charge density wave (CDW) orders in the bilayer kagome metal ScV_6Sn_6 remains a challenge. Experimentally, upon cooling, short-range CDW order with the wave vector 𝐪_2=(1/3,1/3,1/2) is observed, which is subsequently suppressed by the condensation of the long-range CDW order 𝐪_3=(1/3,1/3,1/3) at lower temperature. In conflict with these observations, theoretical calculations overestimate the transition temperature by a few thousand Kelvin and incorrectly predict the 𝐪_2 CDW order to be the ground state. Here, we develop a theory of CDW order in ScV_6Sn_6 based on anharmonic phonon-phonon calculations combined with density functional theory. We predict a temperature-driven phase transition from the high-temperature 𝐪_2 CDW to the low-temperature 𝐪_3 CDW order, fully explaining experimental observations. Additionally, we clarify that both multi-phonon effects and semi-core electron states play a crucial role in stabilizing the 𝐪_3 order. Finally, we construct a phase diagram of the competing CDWs in the lattice parameter space and demonstrate that the out-of-plane lattice parameter plays a pivotal role in manipulating the competing CDWs in ScV_6Sn_6, motivating us to propose compressive bi-axial strain as an experimental protocol to stabilize the 𝐪_2 CDW order. Our work provides a full theory of CDWs in ScV_6Sn_6, rationalizing experimental observations and resolving ealier discrepancies between theory and experiment. Overall, our work contributes to the wider effort of understanding CDWs in the kagome metal family.