Commensurate-to-incommensurate transition of charge-density-wave order and a possible quantum critical point in pressurized kagome metal CsV${}_3$Sb${}_5$

Clarifying the interplay between charge density waves (CDWs) and superconductivity is important in the kagome metal CsV${}_3$Sb${}_5$, and pressure ($P$) can play a crucial role. Here, we present ${}^{121\mathrm{/}123}$Sb nuclear quadrupole resonance (NQR) measurements under hydrostatic pressures up to 2.43 GPa in CsV${}_3$Sb${}_5$ single crystals. We demonstrate that the CDW gradually changes from a commensurate modulation with a star-of-David (SoD) pattern to an incommensurate one with a superimposed SoD and Tri-hexagonal (TrH) pattern stacking along the $c$-axis. Moreover, the linewidth $\delta \nu$ of ${}^{121\mathrm{/}123}$Sb-NQR spectra increases with cooling down to $T_{\mathrm{C}\mathrm{D}\mathrm{W}}$, indicating the appearance of a short-range CDW order due to CDW fluctuations pinned by quenched disorders. The $\delta \nu$ shows a Curie-Weiss temperature dependence and tends to diverge at $P_{\mathrm{c}}\sim$ 1.9 GPa, suggesting that a CDW quantum critical point (QCP) exists at $P_{\mathrm{c}}$ where $T_{\mathrm{c}}$ shows the maximum. For $P>P_{\mathrm{c}}$, spin fluctuations are enhanced when the CDW is suppressed. Our results suggest that the maximal $T_{\mathrm{c}}$ at $P_{\mathrm{c}}\sim$ 1.9 GPa is related to the CDW QCP and the presence of spin fluctuations prevent the $T_{\mathrm{c}}$ from a rapid decrease otherwise after the CDW is completely suppressed.