Unusual nature of fully gapped superconductivity in In-doped SnTe

The superconductor Sn${}_{1-x}$In${}_x$Te is a doped topological crystalline insulator and has become important as a candidate topological superconductor, but its superconducting phase diagram is poorly understood. By measuring about 50 samples of high-quality, vapor-grown single crystals, we found that the dependence of the superconducting transition temperature $T_c$ on the In content $x$ presents a qualitative change across the critical doping $x_c\simeq 3.8\%$, at which a structural phase transition takes place. Intriguingly, in the ferroelectric rhombohedral phase below the critical doping, $T_c$ is found to be strongly enhanced with impurity scattering. It appears that the nature of electron pairing changes across $x_c$ in Sn${}_{1-x}$In${}_x$Te.

Figure 1

Hole density $p$ vs $x$ (lower axis) and $c_{\mathrm{In}}$ (upper axis). The solid line is a least-square fit to the data and the dashed line indicates the approximate hole density for $x=0$–0.017 reported in Ref. 26.

Figure 2

$T_c$ vs $p$ plot with the upper horizontal axis showing $x_{\mathrm{ref}}$. Depending on the sample, $T_c$ was measured either with resistivity (open circles) or with specific heat (open squares). The vertical dashed line marks $p_c$ to separate the two different structure phases. The vertical error bar signifies the transition width, which was defined with the resistivity change from 90% to 10% of ${\rho }_{4\mathrm{K}}$, or with the range between the onset and the peak in the specific-heat jump.

Figure 3

Dependencies of $T_c$ on ${\rho }_{4\mathrm{K}}$ for five $p$ values (in units of ${10}^{20}$ cm${}^{-3}$), 2.8, 3.6, 5.8, 9.2, and 10.5. The first two are in the ferroelectric rhombohedral phase ($p<p_c$), while the last three are in the cubic phase ($p>p_c$).

Figure 4

(a) ${\rho }_{xx}\left(T\right)$ of a sample in the ferroelectric rhombohedral phase ($p<p_c$), $p=3.2\times {10}^{20}$ cm${}^{-3}$ ($x=0.025$); the inset show the sharp superconducting transition at $T_c=1.42$ K. (b) $c_{\mathrm{el}}/T$ vs $T$ of the same sample measured down to 0.34 K in 0 T (red circles) and in 2 T (blue circles). (c), (d) $c_{\mathrm{el}}/T$ vs $T$ plots for samples in the cubic phase ($p>p_c$), $p\simeq 5\times {10}^{20}$ cm${}^{-3}$ ($x\simeq 0.04$, $T_c=1.22$ K) and $p\simeq 7\times {10}^{20}$ cm${}^{-3}$ ($x\simeq 0.05$, $T_c=1.41$ K); those samples were only characterized with specific heat. In (b)–(d), solid lines show the modified BCS fits to the experimental data with tunable $\alpha$, and dashed lines indicate the values of ${\gamma }_{\mathrm{n}}$.