London penetration depth and superfluid density of single-crystalline ${\text{Fe}}_{1+y}\left({\text{Te}}_{1-x}{\text{Se}}_x\right)$ and ${\text{Fe}}_{1+y}\left({\text{Te}}_{1-x}{\text{S}}_x\right)$

The in-plane London penetration depth, $\lambda \left(T\right)$, was measured in single crystals of the iron-chalcogenide superconductors ${\text{Fe}}_{1.03}\left({\text{Te}}_{0.63}{\text{Se}}_{0.37}\right)$ and ${\text{Fe}}_{1.06}\left({\text{Te}}_{0.88}{\text{S}}_{0.14}\right)$ by using a radio-frequency tunnel diode resonator. Similar to the iron-arsenides and in stark contrast to the iron-phosphides, iron-chalcogenides exhibit a nearly quadratic temperature variation of $\lambda \left(T\right)$ at low temperatures. The absolute value of the penetration depth in the $T\to 0$ limit was determined for ${\text{Fe}}_{1.03}\left({\text{Te}}_{0.63}{\text{Se}}_{0.37}\right)$ by using an Al coating technique, giving $\lambda \left(0\right)\approx 560\pm 20\text{nm}$. The superfluid density ${\rho }_s\left(T\right)={\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)$ was fitted with a self-consistent two-gap $\gamma$ model. While two different gaps are needed to describe the full-range temperature variation in ${\rho }_s\left(T\right)$, a nonexponential low-temperature behavior requires pair-breaking scattering, and therefore an unconventional (e.g., $s_{\pm }$ or nodal) order parameter.

Figure 1

(Color online) Main panel: variation in the London penetration depth, $\Delta \lambda \left(T\right)$ for three Fe(Te,Se) samples in the low temperature range shown along with the fitting curves assuming power-low or $s$-wave BCS behavior. The curves for samples #2 and #3 of Fe(Te,Se) are shifted vertically for clarity by 15 and 30 nm, respectively. Inset: $\Delta \lambda \left(T\right)$ for three Fe(Te,Se) samples and one Fe(Te,S) sample.

Figure 2

(Color online) $\Delta \lambda$ plotted vs. ${\left(T/T_c\right)}^2$ for three Fe(Te,Se) crystals in the main panel and Fe(Te,S) crystal in the inset in the temperature range up to $T_c/3$. The curves for Fe(Te,Se), samples #2 and #3, are shifted vertically for clarity by 50 and 25 nm, respectively.

Figure 3

(Color online) Exponent $n$ and prefactor $A$ obtained by fitting to $\Delta \lambda \left(T\right)\propto A{T}^n$ for various upper temperature limits shown on the $x$ axis. The exponents in the upper panel were obtained with $n$ and $A$ both being free parameters. In the lower panel, symbols show $A$ acquired with a fixed $n$, while the dashed lines shows $A$ obtained when $n$ was a free parameter as well.

Figure 4

(Color online) Effective penetration depth in single crystal Fe(Te,Se) before (blue circles) and after (red triangles) coating with an Al layer. The curve is shifted up according to Eq. (1) and the data are extrapolated to $T=0$ using a $T^2$ fit resulting in $\lambda \left(0\right)\approx 560\pm 20\text{nm}$.

Figure 5

(Color online) Superfluid density ${\rho }_s\left(T/T_c\right)$ for Fe(Te,Se) calculated with experimental $\Delta \lambda \left(T\right)$ and $\lambda \left(0\right)=560\text{nm}$. The solid (red) line is a fit to the two-gap $\gamma$ model from $0.45T_c$ to $T_c$. The dashed (blue) line is the fit over the full temperature range. Inset: temperature-dependent superconducting gaps calculated self-consistently during the fitting.