Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$

X-ray diffraction was employed to study the evolution of the charge density wave (CDW) in ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ as a function of copper intercalation in order to clarify the relationship between the CDW and superconductivity. The results show a CDW incommensuration arising at an intercalation value coincident with the onset of superconductivity at around $x=0.055(5)$. Additionally, it was found that the charge density wave persists to higher intercalant concentrations than previously assumed, demonstrating that the CDW does not terminate inside the superconducting dome. A charge density wave peak was observed in samples up to $x=0.091(6)$, the highest copper concentration examined in this study. The phase diagram established in this work suggests that charge density wave incommensuration may play a role in the formation of the superconducting state.

Figure 1

(a)–(d) Simultaneous $L$ cuts of the (1, 1, 7) Bragg peak as well as the ($1/2$, $1/2$, $7/2$) charge density wave superlattice peak for various amounts of copper intercalation in ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$. Data in panels (a)–(d) were taken at 50 K, 11 K, 15 K, and 20 K. respectively. Momentum resolution is indicated with the black line above the peaks.

Figure 2

In-plane and out-of-plane inverse linewidths as a function of copper intercalation, obtained from Gaussian fits to the $H$ and $L$ cuts of the ($1/2$, $1/2$, $7/2+\delta$) superlattice peak. (Inset) $H$ cuts of the ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ CDW superlattice peak at 50 K, 13 K, and 20 K for $x=0$, 0.060(5) and 0.91(6), respectively.

Figure 3

$H$ cuts of the CDW superlattice peak at several temperatures for pure ${\mathrm{TiSe}}_2$ (top) and of ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ with $x=0.060(5)$ (bottom). Intensities are normalized to the incident beam counts. (Insets) Black dots indicate the integrated intensity of the $H$ cuts at various temperatures. The red line is the fit used to obtain the transition temperature.

Figure 4

(Top) The degree of incommensuration along $L$ as a function of copper intercalation. The red points outlining the superconducting dome are taken from Ref. [1]. (Bottom) The phase diagram for ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$, where the blue points were obtained in this study. The red points and the line delineating the superconducting region are from Ref. [1].