Evolution of the Superfluid Density in Infinite-Layer Nickelates

Abstract

Nickelate superconductors provide a valuable new platform for the study of unconventional superconductivity that is complementary to the cuprates. One of the central puzzles about high-temperature superconductors is what factors determine the scale of their superconducting transition temperature ($T_\mathrm{c}$). To address this question for infinite-layer nickelates, we present a systematic mutual inductance study of the superfluid density across the doping-dependent superconducting dome of $\mathrm{Nd}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$. We observe a weak superfluid stiffness that exhibits an approximately square-root correlation with $T_\mathrm{c}$. We also find a strong interplay between Nd magnetism and the superconducting phase, manifested as a substantial low-temperature suppression of superfluid density. These observations highlight the importance of superconducting phase fluctuations in limiting $T_\mathrm{c}$ and unexpectedly strong coupling between the Nd 4$f$ moments and the superfluid.

Figures (4)

• Figure 1: (a) The full temperature dependence of the superfluid density (upper panel, normalized to its maximum value) and the dissipative signal (lower panel) for 10 samples spanning the superconducting dome. The legend describes the Sr doping value. (b) The superfluid density (solid blue line, left axis), dissipative signal (solid red line, arbitrary units), and resistance (solid green line, right axis) as a function of temperature for for a representative Nd$_{0.8625}$Sr$_{0.1375}$NiO$_2$ sample. The dashed black line marks where superfluid stiffness equals thermal fluctuations in terms of energy scale. (c) Temperature dependence of superfluid stiffness near $T_{\mathrm{BKT}}$, with the mean field stiffness, data, and the fit to the stiffness using the renormalization group equations for a representative Nd$_{0.7875}$Sr$_{0.2125}$NiO$_2$ sample.
• Figure 2: (a) The temperature at which the penetration depth reaches its minimum value, $T$($\lambda=\lambda_{\mathrm{min}}$), as a function of Sr doping $x$, showing an approximately linear dependence, with fit line (black) $T(\lambda=\lambda_{\mathrm{min}})=21(0.29-x)$. (b) The ratio of measured superfluid density remaining at base temperature $\lambda(T = 0 \ \mathrm{K})^{-2}$ to its estimated maximum value in the absence of magnetic effects $\lambda_0^{-2}$, as a function of Sr doping. The solid black fit line follows $\lambda_0^2/\lambda_{\mathrm{min}}^2=1- \exp(-(x-0.09)/0.055)$. (c) The superfluid density and the dissipative signal of an underdoped Nd$_{0.88}$Sr$_{0.12}$NiO$_2$ sample, where the maximum superfluid suppression is observed. (d) The full temperature dependence of the superfluid density proxy $\lambda_0^{-2}$ for each doping. For each sample, a pair of dashed black lines shows our quadratic fits obtained for the temperature ranges near $T(\lambda=\lambda_{\mathrm{min}})$ and the onset of the BKT superfluid drop, with the green shade illustrating the range of variation of our estimate. (e) $T_{\mathrm{c}}$ as a function of $T_{\Theta}$, with the color of each marker representing its corresponding Sr doping, following the coloring scheme in panel (a) and (b).
• Figure 3: (a) $\lambda_0^{-2}$ (left, blue) and $T_{\mathrm{c}}$ (right, red) measured as a function of doping across the superconducting dome. (b) Linear plot of $T_{\mathrm{c}}$ against $\lambda_0^{-2}$. A power law fit to the data is shown as a solid black line: $T_{\mathrm{c}} =(10.9 \pm 0.2) \left( \lambda_0^{-2} \right) ^{0.43 \pm 0.03}$. The color of each marker represents its corresponding Sr doping, following the coloring scheme in Fig. \ref{['fig1']} and Fig. \ref{['fig2']}. (c) Log-log plot of $T_{\mathrm{c}}$ against $\lambda_0^{-2}$. The same fit line in panel (b) is shown again as a solid black line.
• Figure 4: a) $T_{\mathrm{c}}$ as a function of $\lambda_0^{-2}$ across doping for Nd$_{1-x}$Sr$_{x}$NiO$_2$ and representative cuprate superconductors: LSCO and YBCO. Solid symbols correspond to bulk samples and open symbols correspond to thin film samples. Black lines are guides to the eye, with the dashed ones corresponding to $T_{\mathrm{c}} \propto \lambda_0^{-2}$ and solid ones to $T_{\mathrm{c}} \propto \sqrt{\lambda_0^{-2}}$. Red diamonds: our Nd$_{1-x}$Sr$_{x}$NiO$_2$ data; Green circles: bozovic2016; Blue squares: zuev2005; Pink triangles: hetel2007; Brown triangles: broun2007; Orange stars: hetel2007; Black circles: uemura1989, converted following zuev2005.