Tuning the Interlayer Spacing of High-$T_c$ Bi-Based Superconductors by Intercalation: Measuring the Penetration Depth and the Two-Dimensional Superfluid Density

Substantial control of the interlayer spacing in Bi-based high temperature superconductors has been achieved through the intercalation of guest molecules between the superconducting layers. Measurements using implanted muons reveal that the penetration depth increases with increasing layer separation while $T_c$ does not vary appreciably, demonstrating that the bulk superfluid density is not the determining factor controlling $T_c$. Our results strongly suggest that for Bi-based high temperature superconductors the superfluid density appearing in the Uemura scaling relation ${\rho }_s\propto T_c$ should be interpreted as the two-dimensional density within the superconducting layers, which we find to be constant for each class of system investigated.

Figure 1

(a) Schematic of the Bi2212 intercalates with molecular groups acting to separate the ${\mathrm{CuO}}_2$ bilayers. (b) TF ${\mu }^{+}\mathrm{SR}$ spectra measured in 40 mT above and below $T_c$ for intercalated Bi2212 with $d=2.61\mathrm{nm}$. The stronger relaxation for $T<T_c$ is caused by the distribution of fields in the vortex lattice. (c) Interlayer-bilayer separation $d$ for each intercalate studied.

Figure 2

(a) Temperature dependence of $B_{\mathrm{rms}}$ for Bi2212 (left) and Bi2201 (right) intercalates with $B_a=5\mathrm{mT}$. Fits are described in the main text. (b) The evolution of $B_{\mathrm{rms}}$ with applied field at $T=5\mathrm{K}$ (Bi2201) and $T=20\mathrm{K}$ (Bi2212) with additional data for pristine Bi2212 obtained from Ref. 16. Fits are shown with a solid line for the range over which the fitting was carried out; extrapolations are shown with a dashed line. The materials with the largest layer separations show markedly different behavior in both temperature and applied field (dotted lines are guides to the eye).

Figure 3

(a) Uemura plot of $T_c$ vs $1/{\lambda }_{ab}^2$ for our compounds. The solid line represents the scaling proposed for the underdoped cuprates [3]. (b) The variation of the penetration depth ${\lambda }_{ab}$ with the inverse layer separation $1/d$ gives a straight line dependence for each series, suggesting the constancy of $d/{\lambda }_{ab}^2(\propto {\rho }_{s2\mathrm{D}})$.