Evolution from three-dimensional charge density wave to one-dimensional stripe order in CsV$_{3-x}$Ti$_x$Sb$_5$

Abstract

Understanding intertwined phases near quantum criticality is a central challenge in correlated electron systems. The kagome metal CsV$_{3-x}$Ti$_x$Sb$_5$ provides a fertile platform to investigate the interplay between charge-density-wave (CDW) and superconductivity. Here, combining x-ray diffraction (XRD) and scanning tunneling microscopy (STM), we uncover a dimensional evolution of the CDW upon Ti substitution. We find that even infinitesimal Ti doping (x = 0.009) completely suppresses the three-dimensional 2 $\times$ 2 $\times$ 4 CDW present in pristine CsV3Sb5, while reducing the remaining 2 $\times$ 2 $\times$ 2 CDW to a quasi-two-dimensional order. With further Ti substitution, although no CDW transition is discernible in resistivity measurements, our XRD and STM data reveal the emergence of a (quasi-)one-dimensional CDW with a short correlation length of $\sim$ 20 $Å$ at x = 0.2. The stripelike CDW undergoes a continuous second-order phase transition, characterized by a gradual increase in intensity and correlation length below $\sim$ 56 K. Our results elucidate the dimensional evolution of CDW order in CsV$_{3-x}$Ti$_x$Sb$_5$ and provide new insight into understanding the unconventional CDWs and their role in kagome superconductors.

Figures (6)

• Figure 1: Superconductivity and CDW in ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_5$. (a) Temperature dependence of the in-plane normalized resistance R/R$_{300 K}$. The superconducting transition temperature $T_{\mathrm{c}}$ is determined by the onset temperature of resistance drop. (b) The derivative electrical resistance dR/dT as a function of temperature. The CDW transition temperature $T_{\mathrm{CDW}}$ was determined by the onset point of dR/dT jump. (c) Temperature dependent of magnetic susceptibilities under zero-field cooling (ZFC) with applied field of 10 Oe along c-axis. The data is corrected by calculating the demagnetization factor. Offset was added for clarity. (d) Phase diagram of ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_5$ crystals. The solid lines indicate the selected Ti doping level in our XRD study.
• Figure 2: XRD measurements of ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_5$ taken at 18 K for four Ti doping levels using a Mo K$_{\alpha}$ x-ray source. (a) $(H, K)$ maps of reciprocal space at $L$ = 10. (b) $(H, L)$ maps of reciprocal space at $K$ = 1. (c) $H$-, $K$- and $L$-cuts of the main Bragg peak at [-1, 0, 10] are shown in the left, middle and right panel, respectively. Intensities are normalized to maximum. Vertical offset are added for clarity. The double peaks in $L$-cut originate from an x-ray source consisting of Mo $K_{\alpha1}$ and $K_{\alpha2}$xq. The solid lines are fits with Gaussian functions.
• Figure 3: XRD measurements of ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_5$ taken at 18 K for four Ti doping levels using a Mo K$_{\alpha}$ x-ray source. (a) $(H, K)$ maps of reciprocal space at $L$ = 11.5. The diffraction point at the center is the leakage from main Bragg peak. (b) $(H, L)$ maps of reciprocal space at $K$ = -0.5. The arc signals in colormaps come from beryllium domes. (c) $H$-, $K$-cuts of [-0.5, 1, 9.5] and $L$-cuts of [1, -0.5, 9.5] are shown in the left, middle and right panel, respectively. Vertical offsets are applied for clarity. $H$-cuts: Gaussian fits for $x = 0.009$ and $0.02$, Lorentzian fit for $x = 0.1$, and a guide-to-the-eye line for $x = 0.2$. $K$-cuts: Gaussian fits for all doping levels. $L$-cuts: Lorentzian fits for $x$ = 0.009, 0.02 and 0.1, and a guide-to-the-eye line for $x$ = 0.2. In the fitting, Lorentz functions are used to capture the stripe-like feature in line profile ScV6Sn6.diffuse.scattering.
• Figure 4: XRD measurements for ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_{x}{\mathrm{Sb}}_5$ with x = 0.1 at 18 K using a Mo K$_{\alpha}$ x-ray source. (a) Schematic of scattering signals in $(H, K)$ maps. Different colors indicate different orientations of electronic correlations. Three representative experimental $(H, K)$ diffraction maps are shown in dotted rectangular box. (b) $(H, L)$ and $(K, L)$ maps at $\bf {q}$ = [1, -0.5, 9.5]. The corresponding $H$-, $K$- and $L$-cut are shown near their colormap, respectively. Solid lines in $H$-cut and $K/L$-cut are fits with Gaussian and Lorentz functions, respectively. The intensity of colormaps was plotted in log scale.
• Figure 5: Observations of three equivalent domains of short-ranged unidirectional charge orders in CsV$_{2.85}$Ti$_{0.15}$Sb$_5$ crystal. (a) STM images showing short-ranged charge orders with multiple nanoscale domains. Right panel: zoom-in images of the areas outlined by green, red, and blue squares in the overview image on the left. Each magnified region displays a dominant unidirectional charge order, aligned predominantly along one of three distinct crystalline directions, as indicated by the black dashed lines. (b) Fourier transform of the zoom-in images in (a), showing the broad peaks around the 1/2 Q$_{\mathrm{Bragg}}$ wave vector along one of the three crystalline directions (marked by colored dashed square). Scanning parameters: bias volage Vs=-50 mV, tunneling current: $I_{\mathrm{t}}$=1 nA; temperature: 0.4 K.