Emergence of Fulde-Ferrell-Larkin-Ovchinnikov phase in FeSe in the BCS-BEC crossover

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, predicted more than a half-century ago, is a highly exotic state of fermionic condensate, in which oscillations of the order parameter emerge in real space. Yet, quest of the FFLO phase has been a challenge for a broad range of scientists, including solid-state, ultracold atomic and high-energy physics. Here, via thermal transport measurements in intense magnetic fields up to 33 T, we present compelling evidence for a distinct high-field superconducting phase in an iron-chalcogenide superconductor FeSe for the field H || ab-plane. A discontinuous downward jump in the quasiparticle thermal transport indicates the presence of a first-order transition line within the superconducting phase. We attribute the high-field phase to the FFLO phase, where planar nodes are formed. We discuss the importance of the extremely small Fermi energies, strong spin-orbit coupling and multiband nature for the FFLO phase in FeSe.