Nodeless two-gap superconducting state in single crystals of the stoichiometric iron pnictide LiFeAs

The variations of in- and inter-plane London penetration depths, $\Delta \lambda (T)$, were measured using a tunnel diode resonator in single crystals of the intrinsic pnictide superconductor LiFeAs. This compound appears to be in the clean limit with a residual resistivity of 4 ($T\to 0$) to 8 ($T_c$) $\mu \Omega \hspace{0.5em}$cm and a residual resistivity ratio of 65 to 35, respectively. The superfluid density ${\rho }_s(T)={\lambda }^2(0)/{\lambda }^2(T)$ is well described by the self-consistent two-gap $\gamma$ model. Together with the previous data, our results support the universal evolution of the superconducting gap from nodeless to nodal upon departure from optimal doping even in clean systems. We also conclude that pair-breaking scattering plays an important role in the deviation of the low-temperature behavior of $\lambda (T)$ from the exponential in Fe-based compounds.

Figure 1

Left axis: resistivity (symbols) along with the second-order polynomial fit from $T_c$ to 50 K used to determine the residual resistivity, $\rho (0)=3.7\hspace{0.5em}\mu \Omega$ cm. Right axis: skin depth $\delta$ measured by TDR, ${\delta }_{\mathrm{TDR}}$, compared to that calculated from resistivity, ${\delta }_{\rho }$. Upper inset: $\rho (T)$ in the full temperature range. Lower inset: TDR data for pristine and air-aged samples.

Figure 2

Main panel: $\Delta {\lambda }_{\mathrm{ab}}(T)$ in three LiFeAs crystals (solid dots) and $\Delta {\lambda }_{c,\mathrm{mix}}(T)$ for sample 2 (crosses). Analysis (shown for sample 1) was done assuming both power-law (solid lines) and exponential (dashed line) $T$ dependences. The data for samples 2 and 3 (shifted vertically for clarity by 10 and 20 nm, respectively) were analyzed in a similar way (see Table ). Inset: comparison of the fit residuals for sample 1 for the power-law and exponential functions.

Figure 3

(a) $\Delta \lambda$ vs $T^{3.1}$ (average exponent $n$ over the three samples), (b) exponent $n$, and (c) prefactor $A$, obtained by fitting to $\Delta \lambda (T)\propto {\mathit{AT}}^n$ for various upper temperature limits shown on the $x$ axis.

Figure 4

Symbols: superfluid density ${\rho }_s(T)$ calculated with $\lambda (0)=200$ nm. Solid lines represent the fit to a two-gap $\gamma$ model, ${\rho }_s=\gamma {\rho }_1+(1-\gamma ){\rho }_2$. Dashed line is a single-gap BCS solution. Upper inset: superconducting gaps ${\Delta }_1(T)$ and ${\Delta }_2(T)$ calculated self-consistently during the fitting. Lower inset: ${\Delta }_1/{\Delta }_2$ as a function of temperature.