Line nodes in the energy gap of superconducting ${\text{BaFe}}_2{\left({\text{As}}_{1-x}{\text{P}}_x\right)}_2$ single crystals as seen via penetration depth and thermal conductivity

We report magnetic penetration depth and thermal-conductivity data for high-quality single crystals of ${\text{BaFe}}_2{\left({\text{As}}_{1-x}{\text{P}}_x\right)}_2\left(T_c=30\text{K}\right)$ which provide strong evidence that this material has line nodes in its energy gap. This is distinctly different from the nodeless gap found for $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ which has similar $T_c$ and phase diagram. Our results indicate that repulsive electronic interactions play an essential role for Fe-based high-$T_c$ superconductivity but that uniquely there are distinctly different pairing states, with and without nodes, which have comparable $T_c$.

Figure 1

(Color online) Relative change in the electronic specific heat $\Delta C/T$ of single crystal ${\text{BaFe}}_2{\left({\text{As}}_{0.67}{\text{P}}_{0.33}\right)}_2$ measured using an ac technique under magnetic fields applied along the $c$ axis. A smooth background determined from an extrapolation of the 14 T data has been subtracted. Temperature dependence of the in-plane resistivity $\rho$ of a crystal from the same batch is also shown. Inset shows the upper critical field $H_{c2}\left(T\right)$ determined from the midpoint of the specific-heat jump at each field (closed circles) and the irreversibility field measured by torque measurements (open square) (Ref. 19). The dashed line is a fit to the Wertharmer-Helfand-Hohenberg formula.

Figure 2

(Color online) (a) The change $\Delta \lambda \left(T\right)\equiv \lambda \left(T\right)-\lambda \left(0\right)$ in the penetration depth of ${\text{BaFe}}_2{\left({\text{As}}_{0.67}{\text{P}}_{0.33}\right)}_2$ along with the data for $\left({\text{Ba}}_{0.45}{\text{K}}_{0.55}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\simeq 33\text{K}\right)$ (Ref. 7). Inset compares the results obtained by the microwave and rf techniques. (b) Normalized superfluid density ${\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)$ as a function of $T/T_c$. The data follow a $T$-linear dependence (dashed line) down to $T/T_c\sim 0.05$. The deviation at lower $T/T_c$ can be fitted to the dependence for a gap with line nodes with disorder (solid line). The upper inset is the data up to $T_c$. The tail near $T_c$ in $\left({\text{Ba}}_{0.45}{\text{K}}_{0.55}\right){\text{Fe}}_2{\text{As}}_2$ is due to the skin depth effect at microwave frequencies (Ref. 7). The lower inset shows $\Delta \lambda \left(T\right)$ at low temperatures in two samples (shifted vertically for clarity).

Figure 3

(Color online) (a) Thermal conductivity divided by temperature $\kappa /T$ is plotted against $T^2$ at zero field (main panel) and on a linear $T$ axis (inset). The solid lines are the fit to the $T^2$ dependence. The reported data of $\left({\text{Ba}}_{0.75}{\text{K}}_{0.25}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\simeq 30\text{K}\right)$ (Ref. 8) and the phonon contribution estimated in ${\text{BaFe}}_2{\text{As}}_2$ (Ref. 23) are also shown. (b) Residual ${\kappa }_0\left(H\right)/T$ vs $H/H_{c2}$. Also shown are the results for ${\text{Tl}}_2{\text{Ba}}_2{\text{CuO}}_{6+\delta }$ (Ref. 27), $\left({\text{Ba}}_{0.75}{\text{K}}_{0.25}\right){\text{Fe}}_2{\text{As}}_2$ (Ref. 8), and Nb (Ref. 28). The gradual increase in $\kappa \left(H\right)/T$ in $\left({\text{Ba}}_{0.75}{\text{K}}_{0.25}\right){\text{Fe}}_2{\text{As}}_2$ has been attributed to the slight modulation of the gap value (Ref. 8). Inset shows the same data in ${\text{BaFe}}_2{\left({\text{As}}_{0.67}{\text{P}}_{0.33}\right)}_2$ plotted against ${\left(H/H_{c2}\right)}^{1/2}$. The line represents the $\sqrt{H}$ dependence.