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Impact of Sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV$_3$Sb$_5$

Ethan T. RitzRafael M. FernandesTuran Birol
Dec 2022
Elucidating the microscopic mechanisms responsible for the charge densitywave (CDW) instability of the AV$_3$Sb$_5$ (A=Cs, K, Rb) family of kagomemetals is critical for understanding their unique properties, includingsuperconductivity. In these compounds, distinct CDW phases with wave-vectors atthe $M$ and $L$ points are energetically favorable, opening the possibility oftuning the type of CDW order by appropriate external parameters. Here, we shedlight on the CDW landscape of CsV$_3$Sb$_5$ via a combination offirst-principles calculations and phenomenology, which consists of extractingthe coefficients of the CDW Landau free-energy expansion from densityfunctional theory. We find that while the main structural distortions of thekagome lattice in the staggered tri-hexagonal CDW phase are along thenearest-neighbor V-V bonds, distortions associated with the Sb ions play adefining role in the energy gain in this and all other CDW states. Moreover,the coupling between ionic displacements from different unit cells is small,thus explaining the existence of multiple CDW instabilities with differentmodulations along the c-axis. We also investigate how pressure and temperatureimpact the CDW phase of CsV$_3$Sb$_5$. Increasing pressure does not change thestaggered tri-hexagonal CDW ground state, even though the $M$-point CDWinstability disappears before the $L$-point one, a behavior that we attributeto the large nonlinear coupling between the order parameters. Upon changing thetemperature, we find a narrow regime in which another transition can takeplace, toward a tri-hexagonal Star-of-David CDW phase. We discuss theimplications of our results by comparing them with experiments on thiscompound.