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We present resistivity and thermal-conductivity measurements ofsuperconducting FeSe in intense magnetic fields up to 35 T applied parallel tothe $ab$ plane. At low temperatures, the upper critical field $\mu_0H_{c2}^{ab}$ shows an anomalous upturn, while thermal conductivity exhibits adiscontinuous jump at $\mu_0 H^{\ast}\approx 24$ T well below $\mu_0H_{c2}^{ab}$, indicating a first-order phase transition in the superconductingstate. This demonstrates the emergence of a distinct field-inducedsuperconducting phase. Moreover, the broad resistive transition at hightemperatures abruptly becomes sharp upon entering the high-field phase,indicating a dramatic change of the magnetic-flux properties. We attribute thehigh-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where theformation of planar nodes gives rise to a segmentation of the flux-linelattice. We point out that strongly orbital-dependent pairing as well asspin-orbit interactions, the multiband nature, and the extremely small Fermienergy are important for the formation of the FFLO state in FeSe.

Evidence for an FFLO state with segmented vortices in the BCS-BEC-crossover superconductor FeSe