Enhanced Critical Currents and Irreversibility Fields in YBa$_2$Cu$_4$O$_8$ Films through Ca-Substitution
The intrinsic carrier concentration of superconducting materials may not be optimal, and different superconducting properties may have distinct optimal doping levels. Here, we show that Ca substitution increases the hole concentration in intrinsically underdoped epitaxial (Y$_{1-x}$Ca$_x$)Ba$_2$Cu$_4$O$_8$ (YCa124) films with $x \leq 0.10$, driving YCa124 toward optimal doping, increasing $T_c$ and $J_c$. At 40 K, 10% Ca doping increases $J_c$ by factors of 2.4 and 10 at 0.03 and 6 T, respectively, compared with the undoped film. The field dependence of $J_c$ follows $J_c \propto B^{-0.5}$, independent of Ca content, indicating that Ca substitution does not alter the dominant pinning mechanism. This field dependence is consistent with pinning by planar Y-125 stacking-fault intergrowths observed by electron microscopy. In addition, Ca substitution slows thermally activated vortex motion (creep) at $T \gtrsim 15$ K, while at lower temperatures the creep rate $S$ shows an unusual decrease with increasing field. Finally, we consider how doping tunes the upper bound on $J_c$, set by the depairing current density $J_d$, and the lower bound on creep, set by the Ginzburg parameter $G_i$. We find positive correlations between $J_c$ and $J_d$, and between $S$ and $G_i$, and compare them with trends across a broad range of superconductors.