Robust Charge-Density Wave Correlations in Optimally-Doped YBa2Cu3Oy

Abstract

Charge-density wave (CDW) order is a key property of high-Tc cuprates, but its boundaries in the phase diagram and potential connections to other phases remain controversial. We report nuclear magnetic resonance (NMR) measurements in the prototypical cuprate YBa2Cu3Oy demonstrating that short-range static CDW order remains robust at optimal doping (p=0.165), exhibiting a strength and temperature dependence in the normal state similar to those observed at p=0.11 in the underdoped regime. For an overdoped sample with p=0.184, we detect no static CDW down to T=Tc, though weak CDW order plausibly emerges below Tc. More broadly, we argue that both quenched disorder and competition with superconductivity influence the apparent boundary of the CDW phase, likely causing an underestimation of its intrinsic extent in doping. These findings challenge the view that the CDW phase boundary lies below p*=0.19, widely regarded as the critical doping where the pseudogap phase ends in YBa2Cu3Oy.

Figures (10)

• Figure 1: Pseudogap temperature $T^*$. (a) Knight shift $K \propto \chi_{\rm spin}$ vs. temperature for O(3) sites in $p=0.165$ (blue) and $p=0.184$ (orange) samples. The rectangles mark the onset of visible decrease of $K$ upon cooling, which defines the pseudogap onset temperature $T^*$. For $p=0.165$, $K$ shows a sharper decrease below 130 - 150 K, i.e. well below $T^*$, which is also where CDW correlations become significant (Fig. \ref{['width']}). This correlation is consistent with recent work indicating that short-range CDW order contributes to the reduction in $\chi_{\rm spin}(T)$Zhou2024. (b) Phase diagram showing that the $T^*$ values are consistent with literature data at other doping levels in YBCO Alloul2012. Notice that superconducting fluctuations are expected to be negligible above approximately 100 K for near-optimally-doped YBCO Grbic2011.
• Figure 2: Evidence for static CDW. (a) Full width at half maximum of each of the four satellite lines, for $p=0.165$ (blue) and $p=0.184$ (orange) samples. (b) Quadrupole contribution to the width $w_{\rm quad}$ relative to the quadrupole frequency $\nu_{\rm quad}=(\nu_{\rm HF1}-\nu_{\rm LF1})/2$ where $\nu_{\rm HF1}$ ($\nu_{\rm LF1}$) is the resonance frequency of the first high (low) frequency satellite. The $T$ dependence of $w_{\rm quad}$ directly reflects the growth of CDW correlations. See End Matter for details on the analysis. The dashed lines guide the eye.
• Figure 3: Illustration of how disorder affects the $T$ dependence of the CDW amplitude (inspired by refs. Straquadine2019Mallayya2024 on an unidirectional CDW in a layered system) and how this impacts the determination of an apparent onset temperature $T_{\rm CDW}$, which can strongly depend on the signal-to-noise ratio (i.e. experimental sensitivity). Many CDW materials, even among those nominally disorder-free, show a small pretransitional tail at high temperature due to disorder (green curve). Cuprates and other materials with off-stoichiometric dopants more often follow the red curve (if not for competing effects due to superconductivity at $T \ll T_{\rm CDW}$).
• Figure 4: $^{17}$O NMR spectra for YBCO $p=0.165$ at 245 K (top) and $p=0.184$ at 151 K (bottom). Because $^{17}$O has a nuclear spin $I=5/2$, there are five resonance lines for each crystallographic site: a central line as well as two low-frequency satellites (named LF1 and LF2) and two high-frequency satellites (HF1 and HF2). For the ideal ortho-I structure, all chains are oxygen full and there are four different crystallographic sites: the apical O(4), the chain O(1) (not seen here due to low $^{17}$O concentration and presumably large broadening at this site) and two planar sites, O(2) and O(3), corresponding to the bonds parallel to the $a$ and $b$ crystallographic axes, respectively, as shown in the top view of a CuO$_2$ plane (right). For $p=0.165$, the magnetic field $B\simeq 9$ T is tilted within the $bc$ plane by an angle $\theta= 16^\circ$ from the $c$ axis to maximize the separation between the regular O(3) lines and the O(3v) lines associated with vacancy nearest neighbors ($\theta= 12^\circ$ for $p=0.184$). The integrated intensity of O(3v) is $22\pm5$% of the total O(3)+O(3v) intensity, roughly consistent with the expect 16% of O(3) first neighbors to $\delta_{\rm v}=0.08$ isolated vacancies. O(3v) and O(4v) sites are not clearly observed in our previous works on underdoped YBCO Wu2013Wu2015Zhou2017PRLVinograd2021Vinograd2019. The asymmetric shape of the lines, also due to oxygen disorder, is distinct from the $B$ and $T$ dependent asymmetry observed for the long-range ordered CDW Zhou2017PRL. The LF2 and HF2 satellites of O(4) are off-scale due to larger quadrupole coupling than other sites. The line assignment is based on earlier works (Wu2015 and refs. therein, and Reichardt2018 for a different perspective on the O(2)-O(3) splitting). The working frequency $f_0$ is 52.0138 MHz.
• Figure 5: Temperature dependence of the magnetization across the superconducting transition $T_c$ for the two samples, as measured in a measured in a superconducting quantum interferometer device (SQUID).