Fully gapped superconductivity in In-doped topological crystalline insulator ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$

Superconductors derived from topological insulators and topological crystalline insulators by chemical doping have long been considered to be candidates as topological superconductors. ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$ is a topological crystalline insulator with mirror symmetry protected surface states on (001)-, (011)-, and (111)-oriented surfaces. The superconductor $({\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}{)}_{0.7}{\mathrm{In}}_{0.3}\mathrm{Te}$ is produced by In doping in ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$, and is thought to be a topological superconductor. Here we report scanning tunneling spectroscopy measurements of the superconducting state as well as the superconducting energy gap in $({\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}{)}_{0.7}{\mathrm{In}}_{0.3}\mathrm{Te}$ on a (001)-oriented surface. The spectrum can be well fitted by an anisotropic $s$-wave gap function of $\mathrm{\Delta }\left(\theta \right)=0.72+0.18cos4\theta$ meV using Dynes model. The results show that the superconductor seems to be a fully gapped one without any in-gap states, in contradiction with the expectation of a topological superconductor.

Figure 1

(a) Theoretically simulated Laue diffraction patterns of the (001)-oriented surface of $({\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}{)}_{0.7}{\mathrm{In}}_{0.3}\mathrm{Te}$. (b) Experimental Laue diffraction patterns from the cleaved surface of a single crystal.

Figure 2

Temperature dependence of the resistivity in a semilogarithmic plot for a $({\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}{)}_{0.7}{\mathrm{In}}_{0.3}\mathrm{Te}$ single crystal. The inset shows the temperature dependence of magnetic susceptibility measured with ZFC and FC processes at an applied field of 10 Oe.

Figure 3

(a) A typical STS spectrum measured at 400 mK. The fitting results are shown in (b)–(f). The symbols represent the experimental data, and the colored lines are the theoretical fits to the data with the Dynes model by (b) $s$ wave, (c) $d$ wave, (d) double $s$ waves, (e) $d+s$ wave, and (f) an anisotropic $s$-wave gap, respectively. The inset in (f) shows a fourfold symmetric gap function $\mathrm{\Delta }\left(\theta \right)=0.72+0.18cos4\theta$ meV yielded from the fitting with an anisotropic $s$-wave gap.

Figure 4

(a) Temperature dependence of tunneling spectra measured from 0.4 to 5 K (symbols) and theoretical fittings (solid lines) by anisotropic $s$-wave gaps. (b) Temperature dependence of maximal gap $({\mathrm{\Delta }}_1+{\mathrm{\Delta }}_2$) value derived by the fittings. The solid line is the result of theoretical calculation using the BCS model by fixing ${\mathrm{\Delta }}_{\max }\left(0\right)$ and $T_{\mathrm{c}}$ derived from our experiment (see text).