Normal-state resistivity and the depairing current density of ${\mathrm{BaFe}}_2{(\mathrm{As},P)}_2$ nanobridges along the $c$ axis

We report precise measurements to obtain the normal-state resistivity and the depairing current density of ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{P}_x\right)}_2(x\sim 0.29-0.32)$ nanobridges along the $c$ axis, by using focused ion beam (FIB) techniques. We obtained both of the $ab$-plane and $c$-axis resistivity $({\rho }_{ab}$ and ${\rho }_c)$ in the same part of a specimen, by fabricating the $c$-axis nanobridge in the middle of a narrow bridge extended in the $ab$ plane, in spite of the slight deficiency of P dopant due to the additional FIB fabrication. The normal-state resistivity anisotropy agreed with the previous results for bulk samples, showing ${\rho }_c/{\rho }_{ab}<8$ just above the superconducting transition temperature, $T_c$, in the slightly underdoped region and a slight decrease with increasing temperatures. The critical current density obtained in the $c$-axis nanobridges near the optimal doping reaches $\sim 8$ $\mathrm{MA}/{\mathrm{cm}}^2$ at $0.15T_c$, corresponding to about 87% of a depairing limit derived by the Eilenberger equations. An extrapolation to $T=0$ K using the Ginzburg-Landau model suggests that the anisotropy of the depairing current density roughly corresponds to that of the normal-state resistivity. At low temperatures, we also observed a steplike voltage jump before arriving at the depairing limit, suggesting the occurrence of phase-slip phenomena near the depairing processes.