3/8 charge-density wave instability in the kagome metal CsV${}_3$Sb${}_5$

The kagome metal CsV${}_3$Sb${}_5$ exhibits charge density wave (CDW) and superconducting transitions, both of which are substantially affected by pressure. Recent x-ray diffraction experiments identify a new charge-ordered phase at a pressure coinciding with the dip of the superconducting dome. This CDW phase displays a distinctive wavevector $\mathbf{Q}=(3\mathrm{/}8,0,1\mathrm{/}2)$ and monoclinic symmetry, in contrast to the $2\times 2\times 2$ and $2\times 2\times 4$ orders reported at ambient pressure. In this letter, we show that density functional perturbation theory (DFPT) calculations on a fine reciprocal-space grid predict the leading lattice instability of CsV${}_3$Sb${}_5$ to be at this wavevector. Finite-displacement calculations reveal that while anharmonic effects stabilize the conventional $L_2^{-}$ CDW at ambient pressure, the competing $3\mathrm{/}8$ instability becomes energetically favorable above $\sim$1 GPa, consistent with experimental observations. Interestingly, the nesting function displays a peak at the same wavevector. A Landau free energy analysis explains the emergence of the monoclinic distortion observed in x-ray diffraction, in addition to several bond-ordering patterns that may be relevant to the observed trends in the superconducting $T_c$.