Superconductivity, pairing symmetry, and disorder in the doped topological insulator ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ for $x\ge 0.10$

The temperature dependence of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ in the superconducting doped topological crystalline insulator ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ was measured down to 450 mK for two different doping levels, $x\approx 0.45$ (optimally doped) and $x\approx 0.10$ (underdoped), bookending the range of cubic phase in the compound. The results indicate no deviation from fully gapped BCS-like behavior, eliminating several candidate unconventional gap structures. Critical field values below 1 K and other superconducting parameters are also presented. The introduction of disorder by repeated particle irradiation with 5 MeV protons does not enhance $T_c$, indicating that ferroelectric interactions do not compete with superconductivity.

Figure 1

Diffraction data verifying single-phase fcc structure in underdoped and optimally doped ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$. In both materials, the lattice constants are consistent with the doping levels as measured through EDS analysis.

Figure 2

(a) Magnetization vs applied magnetic-field sweeps on optimally doped ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ at various temperatures from 1.8 K through 4.0 K, measured in a conventional MPMS SQUID. (b) Magnetization vs temperature sweeps on 10% doped ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ at various fields from 0.1 to 1.8 G, measured in a custom dc SQUID. Isothermal magnetization vs field curves are extracted from these data. In both datasets, $H_p$ is determined as the field for which the magnetization deviates away from being linear in $H$.

Figure 3

TDO measurements showing suppression of superconductivity in applied magnetic fields up to 2.1 T for near-optimally-doped (a) and underdoped (b) ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$.

Figure 4

Critical field $H_{c1}$ (a) and $H_{c2}$ (b) values for underdoped (yellow circles) and near-optimal (red diamonds) ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$. Extrapolated zero-temperature values for $H_{c1}$ are 7.92 and 32.0 G, and for $H_{c2}$ 1.04 and 1.94 T, for underdoped and near-optimal, respectively.

Figure 5

Normalized low-temperature frequency shift $\mathrm{\Delta }f\left(T\right)$ for ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$. The BCS-like fit (red) well describes the data. The inset shows the full, sharp transition, with no evidence of other low-temperature phases.

Figure 6

Normalized low-temperature frequency shift $\mathrm{\Delta }f\left(T\right)$ for ${\mathrm{Sn}}_{0.9}{\mathrm{In}}_{0.1}\mathrm{Te}$. The BCS-like fit (red) well describes the data. The inset shows the full, sharp transition, with no evidence of other low-temperature phases.

Figure 7

Superconducting transitions following repeated irradiations with 5 MeV protons in a crystal of underdoped ${\mathrm{Sn}}_{0.9}{\mathrm{In}}_{0.1}\mathrm{Te}$ ($T_c=1.8$ K) and two crystals of near-optimally-doped ${\mathrm{Sn}}_{0.55}{\mathrm{In}}_{0.45}\mathrm{Te}$ ($T_c=3.8$ and 4.1 K) as measured by TDO and SQUID magnetometry, respectively. With doses up to $2\times {10}^{17}p/{\mathrm{cm}}^2$, there is essentially no change in the transition temperature.