The Nature of the Superconductivity of Tl$_5$Te$_3$

The search for topologically non-trivial states of matter, such as topological insulators, has sparked significant interest in the impact of spin-orbit coupling on strongly correlated electronic behaviors, such as superconductivity. The known compound Tl$_5$Te$_3$ exhibits a superconducting transition at $T_c$ = 2.4 K, and contains heavy elements, making it an ideal compound in which to look for new physics at the intersection between superconductivity and strong spin-orbit coupling. In 1973, Haemmerle et al. conjectured that two-gap superconductivity might explain previous anomalous superconducting volume fractions observed in their polycrystalline samples. We have reinvestigated the superconductivity of Tl$_5$Te$_3$ using magnetic susceptibility, heat capacity, and point contact measurements on powder and single crystal samples, and resolved these previous discrepancies. Further, we report on long-range and local structure determination of superconducting and non-superconducting Tl$_5$Te$_3$ samples, as well as the relationship between structural details and the observed superconductivity.