Thermoelectricity and electronic correlation enhancement in FeS by light Se doping

We report thermoelectric studies of ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x=0,0.06$) superconducting single crystals that feature high irreversibility fields and critical current density $J_c$ comparable to materials with much higher superconducting critical temperatures ($T_c$'s). The ratio of $T_c$ to the Fermi temperature $T_F$ is very small, indicating weak electronic correlations. With a slight selenium substitution on sulfur site in FeS both $T_c/T_F$ and the effective mass $m^{*}$ rise considerably, implying increase in electronic correlation of the bulk conducting states. The first-principle calculations show rise of the density of states at the Fermi level in ${\mathrm{FeS}}_{0.94}{\mathrm{Se}}_{0.06}$ when compared to FeS, which is related not only to Fe but also to chalcogen-derived electronic states.

Figure 1

(a) Single-crystal x-ray diffraction (XRD) patterns of ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x$ = 0, 0.06). Inset shows the crystal structure with the space group $P4/nnm$. (b) Temperature dependence of in-plane resistivity $\rho$(T) for ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x$ = 0, 0.06) single crystals. (c) The enlargement of superconducting transitions at low temperature.

Figure 2

Temperature dependence of in-plane (a) thermopower $S(T$) and (b) $S/T$ for ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x$ = 0 and 0.06) single crystals. (c) The Moriya-Ueda plot: $T_c$ as a function of $T_F$ for indicated superconductors [22, 45, 46]; Four blue solid squares represent ${\mathrm{K}}_{0.64}{\mathrm{Fe}}_{1.44}{\mathrm{Se}}_2, {\mathrm{K}}_{0.70}{\mathrm{Fe}}_{1.55}{\mathrm{Se}}_{1.01}{\mathrm{S}}_{0.99}$ [26] and ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x$ = 0, 0.06).

Figure 3

(a) Field dependence of the Hall resistivity ${\rho }_{xy}$ for ${\mathrm{FeS}}_{0.94}{\mathrm{Se}}_{0.06}$ at various temperatures. (b) Plots of ${\rho }_{xy}$ vs ${\mu }_{0}H$ below 2 T with solid linear fitting curves. (c) Temperature dependence of Hall coefficient $R_H$ derived from linear fit in panel (b) below 2 T.

Figure 4

(a) Temperature dependence of heat capacity $C_{\text{p}}/T$ vs $T^2$ for for ${\mathrm{FeS}}_{1-x}{\mathrm{Se}}_x$ ($x$ = 0 and 0.06) single crystals. The solid curve represents the fittings using $C_{\text{p}}/T=\gamma +\beta T^2$. (b) The low-temperature electronic part $C_e/T$ vs $T^2$ in zero field.

Figure 5

The density of states in the vicinity of the Fermi level of the tetragonal ${\mathrm{Fe}}_{16}{\mathrm{S}}_{16}$ supercell (blue) and the tetragonal ${\mathrm{Fe}}_{16}{\mathrm{S}}_{15}{\mathrm{Se}}_1$ supercell (red) for (a) total; (b) total Fe part; (c) total chalcogen part; and (d) S ion in the ${\mathrm{Fe}}_{16}{\mathrm{S}}_{16}$ supercell (cyan) and Se ion the ${\mathrm{Fe}}_{16}{\mathrm{S}}_{15}{\mathrm{Se}}_1$ supercell (magenta).