BCS-BEC crossover and the topological band structure of Fe(Se,Te)

  Fe_1+ySe_xTe_1-xis a nearly compensated semimetal, where both electron and hole pockets are very shallow, with Fermi energies, ε_F, of only a few meV. We realize the BCS-BEC crossover by tuning the Fermi energy via chemical doping, which permits us to systematically change Δ/ε_Ffrom 0.16 to 0.50, where Δ is the superconducting gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic changes in the SC state electronic dispersion as the system evolves from a BCS to a BEC regime. 

  The same compound has recently emerged as a promising candidate to host topological superconductivity. We show that the small Fermi energy combined with the strong electronic correlations in Fe_1+ySe_xTe_1-xallows a unique situation where a relatively small spin-orbit coupling can lead to topological superconductivity with well isolated Majorana states in the vortex cores.