A comprehensive scenario of the single crystal growth and doping dependence of resistivity and anisotropic upper critical fields in (Ba${}_{1-x}$K${}_x$)Fe${}_2$As${}_2$ ($0.22\le x\le 1$)

Large high-quality single crystals of hole-doped iron-based superconductor (Ba${}_{1-x}$K${}_x$)Fe${}_2$As${}_2$ were grown over a broad composition range $0.22 \leq x \leq 1$ by inverted temperature gradient method. We found that high soaking temperature, fast cooling rate, and adjusted temperature window of the growth are necessary to obtain single crystals of heavily K doped crystals (0.65$\le x\le$ 0.92) with narrow compositional distributions as revealed by sharp superconducting transitions in magnetization measurements and close to 100% superconducting volume fraction. The crystals were extensively characterized by x-ray and compositional analysis, revealing monotonic evolution of the $c$-axis crystal lattice parameter with K substitution. Quantitative measurements of the temperature-dependent in-plane resistivity, $\rho (T)$ found doping-independent, constant within error bars, resistivity at room temperature, $\rho (300K)$, in sharp contrast with significant doping dependence in electron and isovalent substituted BaFe${}_2$As${}_2$ based compositions. The shape of the temperature dependent resistivity, $\rho (T)$, shows systematic doping-evolution, being close to $T^2$ in overdoped and revealing significant contribution of the $T$-linear component at optimum doping. The slope of the upper critical field, $d{H}_{c2}\mathrm{/}dT$, scales linearly with $T_c$ for both $H\parallel c$, $H_{c2,c}$, and $H\parallel ab$, $H_{c2,ab}$. The anisotropy of the upper critical field, $\gamma \equiv H_{c2,ab} / H_{c2,c}$determinednearzero-field$T_c$increasesfrom$\sim$2 to 4-5 with increasing K doping level from optimal $x\sim$0.4 to strongly overdoped $x$=1.