  GeTe is a chemically simple IV-VI semiconductor which bears a rich plethora
of different physical properties induced by doping and external stimuli. These
include, among others, ferromagnetism, ferroelectricity, phase-change memory
functionality, and comparably large thermoelectric figure of merits. Here we
report a superconductor - semiconductor - superconductor transition controlled
by finely-tuned In doping. Our results moreover show the existence of a
critical doping concentration around $x = 0.12$ in Ge$_{1-x}$In$_{x}$Te, where
various properties take either an extremum or change their characters: The
structure changes from polarly-rhombohedral to cubic, the resistivity sharply
increases by orders of magnitude, the type of charge carriers changes from
holes to electrons, and the density of states diminishes at the dawn of an
emerging superconducting phase. By core-level photoemission spectroscopy we
find indications of a change in the In-valence state from In$^{3+}$ to
In$^{1+}$ with increasing $x$, suggesting that this system is a new promising
playground to probe valence fluctuations and their possible impact on
superconductivity.
