  We present a combined experimental and theoretical study of the evolution of
the Fermi surface of the anomalous superconductor Pb$_{1-x}$Tl$_x$Te as a
function of thallium concentration, drawing on a combination of
magnetotransport measurements (Shubnikov de Haas oscillations and Hall
coefficient), Angle Resolved Photoemission Spectroscopy (ARPES), and density
functional theory (DFT) calculations of the electronic structure. Our results
indicate that for Tl concentrations beyond a critical value the Fermi energy
coincides with resonant impurity states in Pb$_{1-x}$Tl$_x$Te, and we rule out
the presence of an additional valence band maximum at the Fermi energy. Through
comparison to non-superconducting Pb$_{1-x}$Na$_x$Te we argue that the presence
of these states at the Fermi energy provides the pairing interaction and thus
also the anomalously high temperature superconductivity in this material.
