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Fermi surface reconstruction in (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (0.44 $\leq x \leq$ 1) probed by thermoelectric power measurements

We report in-plane thermoelectric power measurements on single crystals of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (0.44 $\leq x \leq$ 1). We observe a minimum in the S$|_{T=const}$ versus x at x ~ 0.55 that can be associated with the change in the topology of the Fermi surface, a Lifshitz transition, related to the electron pockets at the center of M point crossing the Fermi level. This feature is clearly observable below ~ 75 K. Thermoelectric power also shows a change in the x ~ 0.8 - 0.9 range, where maximum in the thermoelectric power collapses into a plateau. This Lifshitz transition is most likely related to the reconstruction of the Fermi surface associated with the transformation of the hole pockets at the M point into four blades as observed by ARPES measurements.