Evidence for $s$-wave pairing with atomic scale disorder in the van der Waals superconductor ${\mathrm{NaSn}}_2{\mathrm{As}}_2$

The recent discovery of superconductivity in ${\mathrm{NaSn}}_2{\mathrm{As}}_2$ with a van der Waals layered structure raises immediate questions on its pairing mechanism and underlying electronic structure. Here, we present measurements of the temperature-dependent magnetic penetration depth $\lambda \left(T\right)$ in single crystals of ${\mathrm{NaSn}}_2{\mathrm{As}}_2$ down to $\sim 40$ mK. We find a very long penetration depth $\lambda \left(0\right)=960\mathrm{nm}$, which is strongly enhanced from the estimate of first-principles calculations. This enhancement comes from a short mean free path $\ell \approx 1.7\mathrm{nm}$, indicating atomic scale disorder possibly associated with the valence-skipping states of Sn. The temperature dependence of superfluid density is fully consistent with the conventional fully gapped $s$-wave state in the dirty limit. These results suggest that ${\mathrm{NaSn}}_2{\mathrm{As}}_2$ is an ideal material to study quantum phase fluctuations in strongly disordered superconductors with its controllable dimensionality.

Figure 1

Inset: The temperature dependence of resonant frequency shift in a range of $T<1.5\mathrm{K}$ for a single crystal of ${\mathrm{NaSn}}_2{\mathrm{As}}_2$ measured with the TDO system. The transition temperature $T_c=1.18\mathrm{K}$ is determined as the midpoint of the total shift. Main panel: The change of the magnetic penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ normalized by $\mathrm{\Delta }\lambda \left(0.5T_c\right)$ as a function of normalized temperature $T/T_c$. The blue solid and yellow dashed lines represent the fitting curves with power-law and fully gapped functions, respectively.

Figure 2

(a) Upper critical field determined by zero resistivity with applied magnetic fields in the $ab$ plane (orange triangles) and along the $c$ axis (cyan triangles). The dashed lines represent approximate WHH curves for each data. For comparison, the zero resistivity $H_{c2}$ for $H\parallel c$ estimated from the data from Ref. [1] is also plotted (cyan squares). (b) The green symbols are the values of $|{\rho }_s^{\prime }\left(1\right)|/{\lambda }^2\left(0\right)$ as a function of $\lambda \left(0\right)$. The gray band shows a range for the right-hand side of Eq. (1) with corresponding errors. (c) The green dots represent the superfluid density ${\rho }_s\left(T\right)$ calculated with $\lambda \left(0\right)=960\mathrm{nm}$. The black dashed lines are the theoretical curves of single-gap BCS superconductors in the clean limit, and the gray solid line is that in the dirty limit.

Figure 3

(a) The electronic band structure of ${\mathrm{NaSn}}_2{\mathrm{As}}_2$ obtained by the DFT calculations. (b) Brillouin zone of rhombohedral lattice and high symmetry points. (c) The calculated Fermi surface of ${\mathrm{NaSn}}_2{\mathrm{As}}_2$.

Figure 4

Inset: Temperature dependence of resistivity $\rho \left(T\right)$ of the pristine and irradiated samples (with a dose of 0.585 C/${\mathrm{cm}}^2$). Main panel: The green, red, and blue symbols represent $\mathrm{\Delta }\lambda \left(T\right)/\mathrm{\Delta }\lambda \left(0.5T_c\right)$ of pristine and irradiated samples with different $T_c$ values (1.18, 1.11, and 1.08 K), respectively.