Shallow pockets and very strong coupling superconductivity in FeSe$_x$Te$_{1-x}$

The celebrated BCS theory has been successful in explaining metallic superconductors, yet many believe that it must be modified to deal with the newer high temperature superconductors. A possible extension is provided by the BCS-BEC theory, describing a smooth evolution from a system of weakly-interacting pairs to a BEC of molecules of strongly-bounded fermions. Despite its appeal, spectroscopic evidence for the BCS-BEC crossover was never observed in solids. Here we report electronic structure measurements in FeSe$_x$Te$_{1-x}$ showing that these materials are in the BCS-BEC crossover regime. Above $T_c$ we find multiple bands with remarkably small values for the Fermi energy $\varepsilon_F$. Yet, in the superconducting state, the gap $\Delta$ is comparable to $\varepsilon_F$. The ratio $\Delta/\varepsilon_F\approx 0.5$ is much larger than found in any previously studied superconductor, resulting in an anomalous dispersion of the coherence peak very similar to that found in cold Fermi gas experiments, in agreement with the predictions of the BCS-BEC crossover theory.