Thermoelectric power of Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$: possible changes in Fermi surface with and without changes in electorn count

Temperature-dependent, in-plane, thermoelectric power (TEP) data are presented for Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ ($0\le x \le 0.36$) single crystals. The previously outlined by resistivity and susceptibility $x - T$ phase diagram for this system is confirmed. The analysis of TEP evolution with Ru-doping suggests two concentrations, $ x\sim 7\%$ and $x\sim 30\%$ of Ru-doping levels, near which significant changes in the electronic structure, correlations and/or scattering occur. These results are compared with an extended set of TEP data for the electron doped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($0.13\le x \le 0.42$) single crystals. An analysis of TEP data for Co-doping in the overdoped region suggests two more concentrations, $x\sim 11\%$ and $x\sim 22\%$, in addition to x$\sim 2\%$ previously reported, where Lifshitz transition might occur. These data for Co-doping were recently confirmed by ARPES measurements.