Signatures of quantum criticality in the thermopower of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

We demonstrate that the thermopower ($S$) can be used to probe the spin fluctuations (SFs) in proximity to the quantum critical point (QCP) in Fe-based superconductors. The sensitivity of $S$ to the entropy of charge carriers allows us to observe an increase of $S/T$ in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ close to the spin-density-wave (SDW) QCP. This behavior is due to the coupling of low-energy conduction electrons to two-dimensional SFs, similar to heavy-fermion systems. The low-temperature enhancement of $S/T$ in the Co substitution range $0.02<x<0.1$ is bordered by two Lifshitz transitions, and it corresponds to the superconducting region, where a similarity between the electron and nonreconstructed hole pockets exists. The maximal $S/T$ is observed in proximity to the commensurate-to-incommensurate SDW transition, for critical $x_c\approx 0.05$, close to the highest superconducting $T_c$. This analysis indicates that low-$T$ thermopower is influenced by critical spin fluctuations which are important for the superconducting mechanism.

Figure 1

The behavior of $S/T$ vs $\ln T$ in three Co substitution regimes: (a) SDW phase in which the Fermi surface is reconstructed, (b) superconducting, and (c) toward the Fermi liquid at high $x$. The dotted lines emphasize linearity on a $\log T$ scale. Thermopower data are taken from Refs. 44 and 45.

Figure 2

Plot of the slope $n$ of the logarithmic temperature dependence of $S/T$ as a function of Co substitution $x$ shows an increase close to the quantum critical point.

Figure 3

$S/T$ increases when approaching the QCP around $x_c\approx 0.05$, and the parameter $\delta$ (the mass of SF) is decreasing simultaneously with a decrease of $E_F$. The increase of $S/T$ is achieved by decreasing $\delta$ with lowering temperature. In the AF phase the drop is more abrupt, similar to theoretical calculations (Ref. 23).

Figure 4

The contour plot of $S/T$ as a function of $\log T$ and Co substitution $x$ shows a low-$T$ increase due to spin fluctuations in the region of similar nonreconstructed electron $X$ and hole $\Gamma$ pockets, in the $x$ range between the first (LT1) and second (LT2) Lifshitz transitions. The top insets represent the scheme of Fermi-surface topology for each region in the phase diagram delimited by the Lifshitz transitions (taken from Ref. 37). The lower inset emphasizes the similarity between the translated electron and hole pockets (solid and open symbols, respectively), which can lead to the hot regions at the FS (as reported in Ref. 36). The temperatures of the superconducting ($T_c$), structural ($T_S$), and antiferromagnetic ($T_M$) transitions are taken from Refs. 55, and 56. The region of the incommensurate SDW is indicated by $T_{\text{IC}}$ (Ref. 43).

Figure 5

Superconducting transition $T_c$, specific heat jump $C_p/T_c$, and thermopower ($S/T$) at $T=25$ K as a function of concentration $x$ in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$. Specific heat data are from Ref. 73. Lines serve as a guide to the eye.