Examining the low energy electrodynamics of the superconductor-insulator transition in the potential topological superconductor Tl$_4$(Tl$_{1-x}$Sn$_x$)Te$_3$

The search for an intrinsic single crystal topological superconductor is one of the most dynamic areas of modern condensed matter physics. One of the best candidates of such a material is Tl$_5$Te$_3$ (T$_c = 2.3$K), which previous ARPES measurements have shown possesses a Dirac cone within its superconducting gap. However, the fundamental nature of superconductivity, i.e. the superconducting order parameter, in Tl$_5$Te$_3$ remains unknown. Additionally, it has been shown that Tl$_5$Te$_3$ undergoes a superconducting-insulator transition upon doping with Sn. With no band parity inversion expected in the fully Sn doped compound one expects a topological supercondutor - trivial insulator transition, the nature of which is also unknown. In this work we use highly sensitive microwave cavity perturbation measurements, a direct probe of the superfluid density, to study the low energy electrodynamics of superconductivity in Tl$_5$Te$_3$ and its corresponding superconductor-insulator transition upon Sn doping.