superconductors*

The BCS-BEC crossover from strongly overlapping Cooper pairs to non-overlapping
composite bosons in the strong coupling limit has been a long-standing issue of interacting many-body fermion systems. It has been extremely challenging to realize such a crossover state in electronic systems over the past decade. Recently, FeSe semimetal emerged as a high-T_c superconductor located in the BCS-BEC crossover regime, owing to its very small Fermi energies. In FeSe, however, an ordinary BCS-like heat-capacity jump is observed at T_c, posing a fundamental question on the characteristics of the BCS-BEC crossover. Here we report on high resolution heat capacity, magnetic torque, and scanning tunneling spectroscopy measurements in FeSe_1-xS_x. When the nematic order is suppressed at x > 0.17, an unusual BEC-like transition is found in the thermodynamic quantities with giant superconducting fluctuations extending far above T_c. However, no pseudogap formation is observed in the tunneling spectra. These results illuminate highly unusual features of the BCS-BEC crossover in superconductors with multiband electronic structure and competing electronic instabilities.