Signatures of Amorphous Shiba State in FeTe_0.55Se_0.45

The iron-based superconductor FeTe_0.55Se_0.45 is a peculiar material: it hosts surface states with a Dirac dispersion, is a putative topological superconductor hosting Majorana modes in vortices, and has an unusually low Fermi energy. The superconducting state is generally characterized by three gaps in different bands, with the homogeneous, spatially extended Bogoliubov excitations─in this work, we uncover evidence that it is instead of a very different nature. Our scanning tunneling spectroscopy data show several peaks in the density of states above a full gap, and by analyzing their spatial and junction-resistance dependence, we conclude the peaks above the first one are not coherence peaks from different bands. Instead, comparisons with our simulations indicate they originate from generalized Shiba states that are spatially overlapping. This can lead to an amorphous state of Bogoliubov quasiparticles, reminiscent of impurity bands in semiconductors. We discuss the origin and implications of this new state.