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

We report in-plane thermoelectric power measurements on single crystals of $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2\left(0.44\le x\le 1\right)$. We observe a minimum in the ${S|}_{T=\text{const}}$ versus $x$ at $x\sim 0.55$ 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 $\sim 75$ K. Thermoelectric power also shows a change in the $x\sim 0.8–0.9$ range, where the 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.

Figure 1

$c$-lattice parameter of $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystals as a function of K concentration. For comparison, the data from Refs. [28] (squares) and [31] (triangles) are also given. The data were collected on the same samples as were used for the thermoelectric power measurements. The inset shows an offset criterion used to determine $T_c$. The arrow denotes a $T_c$ for $x\sim 0.44$.

Figure 2

Thermoelectric power $S$ and $S/T$ (inset) data as a function of temperature of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ single crystals.

Figure 3

Thermoelectric power $S$ as a function of temperature of $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2\left(0.44\le x\le 1\right)$ single crystals on (a) linear and (b) semilogarithmic scales.

Figure 4

$S$ at constant temperatures of 40, 50, 75, 125, and 200 K as a function of potassium concentration of $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2\left(0.44\le x\le 1\right)$ single crystals. The arrows mark a minimum at $x\sim 0.55$ and a small feature at $x\sim 0.8$.

Figure 5

Contour plot of $S$ as a function of temperature and K concentration. Open symbols show $T_c$ values that were determined using the offset criterion shown in the inset to Fig. 1. The dotted lines (as well as the two vertical axes of the edges) show where the existing data for the K concentrations were measured. The region where the broad maximum in the $S\left(T\right)$ data evolves into a plateau is seen as an evolution from the red-yellow into green region at $x\sim 0.8–0.9$.

Figure 6

$S_0$ and $\alpha$ as a function of K concentration. $S_0$ and $\alpha$ are the results of the linear fit, $S$ = $S_0-\alpha T$, to $S\left(T\right)$ over $250\text{K}<T<300$ K.

Figure 7

Thermoelectric power $S$ as a function of temperature of $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystals scaled based on the linear fit, $S$ = $S_0-\alpha T$, over $250\text{K}<T<300$ K. The inset shows the $100\text{K}\le T\le 300$ K data on an enlarged scale. For clarity of the data, every sixth data point is plotted and the superconducting region is excluded.