Planckian scattering and parallel conduction channels in the iron chalcogenide superconductors FeTe$_{1-x}$Se$_x$

The remarkable linear in temperature resistivity of the cuprate superconductors, which extends in some samples from $T_c$ to the melting temperature, remains unexplained. Although seemingly simple, this temperature dependence is incompatible with the conventional theory of metals that dictates that the scattering rate, $1/\tau$, should be quadratic in temperature if electron-electron scattering dominates. Understanding the origin of this temperature dependence and its connection to superconductivity may provide the key to pick the lock of high-temperature superconductivity. Using time-domain terahertz spectroscopy (TDTS) we elucidate the low temperature conducting behavior of two FeTe$_{1-x}$Se$_x$ (FTS) samples, one with almost equal amounts of Se and Te that is believed to be a topological superconductor, and one that is more overdoped. Constrained with DC resistivity, we find two conduction channels that add in parallel, a broad one in frequency with weak temperature dependence and a sharper one whose scattering rate goes as the Planckian limited rate, $\sim kT/h$. Through analysis of its spectral weight we show the superconducting condensate is mainly drawn from the channel that undergoes this Planckian scattering.