Charge Density Wave Order and Fluctuations above $T_{\mathrm{CDW}}$ and below Superconducting $T_c$ in the Kagome Metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$

The phase diagram of the kagome metal family $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) features both superconductivity and charge density wave (CDW) instabilities, which have generated tremendous recent attention. Nonetheless, significant questions remain. In particular, the temperature evolution and demise of the CDW state has not been extensively studied, and little is known about the coexistence of the CDW with superconductivity at low temperatures. We report an x-ray scattering study of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ over a broad range of temperatures from 300 to $\sim 2\mathrm{K}$, below the onset of its superconductivity at $T_c\sim 2.9\mathrm{K}$. Order parameter measurements of the $2\times 2\times 2$ CDW structure show an unusual and extended linear temperature dependence onsetting at $T^{*}\sim 160\mathrm{K}$, much higher than the susceptibility anomaly associated with CDW order at $T_{\mathrm{CDW}}=94\mathrm{K}$. This implies strong CDW fluctuations exist to $\sim 1.7\times T_{\mathrm{CDW}}$. The CDW order parameter is observed to be constant from $T=16$ to 2 K, implying that the CDW and superconducting order coexist below $T_c$, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below $T_c$, if at all. Anomalies in the temperature dependence in the lattice parameters coincide with $T_{\mathrm{CDW}}$ for $c(T)$ and with $T^{*}$ for $a(T)$.

Figure 1

The crystal structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is shown. (a) shows a projection of the structure within the kagome plane, while (b) shows a more three-dimensional perspective. Two Sb sites with different Wyckoff positions are labeled as Sb1 and Sb2.

Figure 2

Magnetic susceptibility measurements for single crystals of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ with an external magnetic field applied within the kagome plane (a),(b) and perpendicular to it (c),(d) are shown. (a),(c) Magnetic susceptibility measurements with ${\mu }_{0}H=1\mathrm{T}$ show an anomaly at $T_{\mathrm{CDW}}=94\mathrm{K}$. The inset shows another anomaly at $\sim 60\mathrm{K}$ in (c) only, field out of plane. (b),(d) Susceptibility measurements at low temperatures using a small dc field ${\mu }_{0}H=1\mathrm{mT}$ show the onset of superconductivity below $T_c=2.9\mathrm{K}$.

Figure 3

The temperature dependence of the specific heat $C_p$ measured at zero field shows a clear transition at $T_{\mathrm{CDW}}=94\mathrm{K}$. The red curve shows a fit to the lattice contribution of $C_p$ using a Thirring model. The subtracted data $\mathrm{\Delta }{C}_p$ are shown at the bottom with its scale on the right $y$ axis. The inset depicts the low-temperature regime to $C_p$, highlighting the onset of superconductivity below $T_c=2.9\mathrm{K}$.

Figure 4

The temperature dependence of the x-ray diffraction intensity (normalized to counts per second) at $[1.5,1.5,L]$ is shown. (a) and (c) show the CDW peaks at $L=-0.5$ and $L=0.5$, respectively, and intensity is plotted on a linear scale. (b) shows the full $[1.5,1.5,L]$ scans, with intensity plotted on a log scale. The temperature-dependent peaks at half-integer reflections $[1.5,1.5,\pm 0.5]$ are due to the $2\times 2\times 2$ CDW structure.

Figure 5

(a) The temperature dependence of the x-ray diffraction scans across $[1.5,1.5,L]$ is shown for temperatures below 20 K and with intensity on a logarithmic scale. (b) The temperature dependence of the integrated peak intensity at the $[1.5,1.5,\pm 0.5]$ CDW reflections, the order parameter, is shown. The inset shows the peak intensity at $[1.5,1.5,0.5]$ at low temperatures, from 2 to 10 K.

Figure 6

The relative change in the lattice constants as a function of the temperature in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ are shown. (a) The $a$ lattice constant shows a slope change at temperatures below $T^{*}\sim 160\mathrm{K}$ and perhaps a second one below $T_{\mathrm{CDW}}=94\mathrm{K}$. (b) The $c$ lattice constant shows an abrupt change roughly coincident with $T_{\mathrm{CDW}}=94\mathrm{K}$. All straight lines are intended as guides to the eye.