Revealing the competition between charge-density wave and superconductivity in CsV${}_3$Sb${}_5$ through uniaxial strain

Abstract

In this paper we report the impact of uniaxial strain $\epsilon$ applied along the crystalline $a$ axis on the newly discovered kagome superconductor CsV${}_3$Sb${}_5$. At ambient conditions, CsV${}_3$Sb${}_5$ shows a charge-density wave (CDW) transition at $T_{\mathrm{CDW}}=94.5$ K and superconducts below $T_C=3.34$ K. In our study, when the uniaxial strain $\epsilon$ is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\sim 33\%$ from 3.0 K to 4.0 K, giving rise to the empirical relation $T_C(\epsilon )=3.4+0.56\epsilon +0.12{\epsilon }^2$. On the other hand, for $\epsilon$ changing from $-0.76\%$ to $1.26\%$, $T_{\mathrm{CDW}}$ decreases monotonically by $\sim 10\%$ from 97.5 K to 87.5 K with $T_{\mathrm{CDW}}(\epsilon )=94.5-4.72\epsilon -0.60{\epsilon }^2$. The opposite response of $T_C$ and $T_{\mathrm{CDW}}$ to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$-axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_C$ with decreasing $c$ is caused primarily by the suppression of $T_{\mathrm{CDW}}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{\mathrm{CDW}}$ with respect to the changes in the $c$-axis arises from the impact of the latter on the trilinear coupling between the $M_1^{+}$ and $L_2^{-}$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV${}_3$Sb${}_5$.

8 pages, 5 figures