\textbf{Resonance-state-induced superconductivity at high Indium contents in In-doped SnTe}

We report a reinvestigation of superconducting Sn$_{\mathrm{1-x}}$In$_{\mathrm{x}}$Te at both low and high In doping levels. Analysis of the superconductivity reveals a fundamental change as a function of $x$: the system evolves from a weakly coupled to a strongly coupled superconductor with increasing indium content. Hall Effect measurements further show that the carrier density does not vary linearly with Indium content; indeed at high Indium content, the samples are overall n-type, which is contrary to expectations of the standard picture of In$^{\mathrm{1+}}$ replacing Sn$^{\mathrm{2+}}$ in this material. Density functional theory calculations probing the electronic state of In in SnTe show that it does not act as a trivial hole dopant, but instead forms a distinct, partly flled In 5s - Te 5p hybridized state centered around E$_{\mathrm{F}}$, very different from what is seen for other nominal hole dopants such as Na, Ag, and vacant Sn sites. We conclude that superconducting In-doped SnTe therefore cannot be considered as a simple hole doped semiconductor.