Static charge-density-wave order in the superconducting state of ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$

Charge-density-wave (CDW) correlations feature prominently in the phase diagram of the cuprates, motivating competing theories of whether fluctuating CDW correlations aid superconductivity or whether static CDW order coexists with superconductivity in inhomogeneous or spatially modulated states. Here we report Cu $L$-edge resonant x-ray photon correlation spectroscopy measurements of CDW correlations in superconducting ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$, $x=0.11$. Static CDW order is shown to exist in the superconducting state at low temperatures and to persist up to at least 85% of the CDW transition temperature. We discuss the implications of our observations for how nominally competing order parameters can coexist in the cuprates.

Figure 1

Doping phase diagram for ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ reproduced from Ref. [23] showing regions with superconductivity (in blue) and how superconductivity (SC) is suppressed around $x=0.125$ coincident with strongest CDW correlations. A vertical black dotted line marks the $x=0.11$ doping level studied here, which we compare with $x=0.125$ (red dotted line).

Figure 2

Speckle patterns for ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ with (a) $x=0.11$ and (b) $x=0.125$ [24] taken at base temperatures of 10 and 15 K, respectively. The data are averaged over (a) 120 and (b) 165 min. We see that the CDW for $x=0.11$ has a significantly shorter correlation length of $150\left(8\right)$ Å compared to $230\left(10\right)$ Å for $x=0.125$. The horizontal direction in the images is approximately parallel to the $K$ direction in reciprocal space following the scale bars shown in white. Lines of reduced intensity are artifacts from the beamstop.

Figure 3

(a) Temperature dependence of the magnetic susceptibility measured in 1 mT applied field (after zero field cooling) for $x=0.11$ and $x=0.125$ samples. No demagnetization correction has been applied. (b) The relative CDW peak intensity, $r$, defined as the intensity of the CDW scattering to the total (peak plus fluorescent) intensity. Error bars on the $x=0.11$ data represent the sum of the standard deviation of the peak intensity parameter obtained by least-squares fitting and a 6% uncertainty coming from variations in the scattering intensity from different spots on the sample, as estimated by comparing repeats of nominally equivalent measurements. The $x=0.125$ data is taken from Ref. [24].

Figure 4

Waterfall plots showing the evolution of a line cut through the center of the CDW speckle pattern as a function of time at (a) 10.5 K, (b) 17.7 K, and (c) 40.0 K. Vertical streaks are indicative of static CDW domains between 10.5 and 40.0 K. The vertical axis is binned into 5 min time periods.

Figure 5

One-time correlation function, $g_2\left(\tau \right)-1$ for different sample temperatures. The curves are flat up to at least 100 min indicating static CDW correlations up to at least this timescale. We assign the small drop off in $g_2$ at longer timescales to finite beamline stability as explained in the text. Lower $g_2(\tau \to 0)$ values at high temperatures are consistent with reduced signal-to-background ratio, with no evidence for CDW fluctuations.