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Effect of controlled point-like disorder induced by 2.5 MeV electron irradiation on nematic resistivity anisotropy of hole-doped (Ba,K)Fe$_2$As$_2$

In-plane anisotropy of electrical resistivity was studied in samples of the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ in the composition range $0.21 \leq x \leq 0.26$ where anisotropy changes sign. Low-temperature ($\sim$20~K) irradiation with relativistic 2.5 MeV electrons was used to control the level of disorder and residual resistivity of the samples. Modification of the stress-detwinning technique enabled measurements of the same samples before and after irradiation, leading to conclusion of anisotropic character of predominantly inelastic scattering processes. Our main finding is that the resistivity anisotropy is of the same sign irrespective of residual resistivity, and remains the same in the orthorhombic $C_2$ phase above the re-entrant tetragonal transition. Unusual $T$-linear dependence of the anisotropy $Δρ\equiv ρ_a(T)-ρ_b(T)$ is found in pristine samples with $x=$0.213 and $x=$0.219, without similar signatures in either $ρ_a(T)$ or $ρ_b(T)$. We show that this feature can be reproduced by a phenomenological model of R.~M.~Fernandes {\it et al.} Phys. Rev. Lett. {\bf 107},217002 (2011). We speculate that onset of fluctuations of nematic order on approaching the instability towards the re-entrant tetragonal phase contributes to this unusual dependence.