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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 highsoaking temperature, fast cooling rate, and adjusted temperature window of thegrowth are necessary to obtain single crystals of heavily K doped crystals(0.65$\leq x \leq$ 0.92) with narrow compositional distributions as revealed bysharp superconducting transitions in magnetization measurements and close to100% superconducting volume fraction. The crystals were extensivelycharacterized by x-ray and compositional analysis, revealing monotonicevolution 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 atroom temperature, $\rho(300K)$, in sharp contrast with significant dopingdependence in electron and isovalent substituted BaFe$_2$As$_2$ basedcompositions. The shape of the temperature dependent resistivity, $\rho(T)$,shows systematic doping-evolution, being close to $T^2$ in overdoped andrevealing significant contribution of the $T$-linear component at optimumdoping. The slope of the upper critical field, $d H_{c2}/dT$, scales linearlywith $T_c$ for both $H\parallel c$, $ H_{c2,c}$, and $H \parallel ab$,$H_{c2,ab}$. The anisotropy of the upper critical field, $\gamma \equivH_{c2,ab} / H_{c2,c}$ determined near zero-field $T_c$ increases from $\sim$2to 4-5 with increasing K doping level from optimal $x \sim$0.4 to stronglyoverdoped $x$=1.

physical review. b, condensed matter and materials physics

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$_2$ ($0.22 \leq x \leq 1$)