Coincident onset of charge-density-wave order at a quantum critical point in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$

The recently demonstrated x-ray scattering approach using a free electron laser with a high field pulsed magnet has opened new opportunities to explore the charge-density-wave (CDW) order in cuprate high temperature superconductors. Using this approach, we substantially degrade the superconductivity with magnetic fields up to 33 T to investigate the onset of CDW order in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ at low temperatures near a putative quantum critical point (QCP) at $p_1\sim 0.08$ holes per Cu. We find no CDW can be detected in a sample with a doping concentration smaller than $p_1$. Our results indicate that the onset of the CDW ground state lies inside the zero-field superconducting dome, and broken translational symmetry is associated with the putative QCP at $p_1$.

Figure 1

CDW in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x, x=6.48$ ($p=0.09$). (a) The upper panel shows the scattering intensity map in the $kl$ plane at $h=0$ taken at $T=T_c$ in the absence of any magnetic field. The white dashed box indicates the location for the quasi-2D CDW. The lower panel shows the averaged intensity from $l=0.3$ to 0.7 r.l.u. The red curve is a Gaussian fit to the peak profile with a linear background (gray line). The inset show the background subtracted averaged intensity. (b) Same as (a), but the data were taken in the superconducting state at $T=10$ K. The black line in the inset is a guide to the eye for zero intensity. (c) The upper panel shows the difference map in the $kl$ plane at $h=0$ obtained by subtracting the data taken at $H=0$ T from the $H=30$ T data. The measurement temperature is 10 K. The lower panels show the averaged intensity of difference maps from $l=0.8$ to 1.2 r.l.u. at representative magnetic fields, which are vertically shifted for visual clarity. The red curves are Gaussian fits to peak profiles.

Figure 2

CDW in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x, x=6.43$ ($p=0.08$). (a) Averaged intensity between $l=0.3$ to 0.7 r.l.u. in the $kl$ plane at $h=0$ taken at zero magnetic field at $T=T_c$ (upper) and at $T=10$ K (lower, black markers). The averaged intensity taken at $T=10$ K and $H=33$ T is also plotted as the red markers in the lower panel. The intensity profiles after removing the background are shown in insets in which the black line serves as a guide to the eye for zero intensity. (b) The upper panel shows the difference map in the $kl$ plane at $h=0$ obtained by subtracting the data taken at $H=0$ T from the $H=33$ T data. The measurement temperature is 10 K. The lower panel shows the averaged intensity of the difference map from $l=0.4$ to 1.2 r.l.u.. The red curve is a Gaussian fit to the peak profile.

Figure 3

Doping dependence of the integrated peak intensity that is obtained by computing the peak area in the averaged peak profile [as defined for the lower panel of Fig. 2(b)]. The integrated peak intensity reflects the CDW amplitude ${\mathrm{\Delta }}_{\text{CDW}}$. The black dashed curve is a guide to the eye. Insets show difference maps in the $kl$ plane at $h=0$ for three representative doping concentrations. These maps were obtained by subtracting data taken at $H=0$ T from the $H\sim 30$ T data. The data for $p\ge 0.1$ were obtained from the same date set published in Ref. [17].

Figure 4

A sketch of the YBCO phase diagram in the heavily underdoped regime with several other measurements superimposed. $T_c$ ($H=0$) (gray curve) is the SC transition temperature at zero magnetic field. The orange shaded regions are the SC region at $H=30$ T [7]. $T_{\mathrm{SDW}}$ is the transition temperature of SDW measured by INS [26]. $T_L$ is the temperature scale at which Hall coefficient changes to negative [1]. $T_V$ is the onset temperature of the anomaly observed in sound velocity [24]. The data shown in Fig. 3 is plotted in the orthogonal plane to the phase diagram.