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There is growing evidence that the superconducting semimetal FeSe ($T_c\sim8$K) is in the crossover regime between weak-coupling Bardeen-Cooper-Schrieffer(BCS) and strong-coupling Bose-Einstein-condensate (BEC) limits. We report onlongitudinal and transverse thermal conductivities, $\kappa_{xx}$ and$\kappa_{xy}$, respectively, in magnetic fields up to 20 T. The fielddependences of $\kappa_{xx}$ and $\kappa_{xy}$ imply that a highly anisotropicsmall superconducting gap forms at the electron Fermi-surface pocket whereas amore isotropic and larger gap forms at the hole pocket. Below $\sim1.0$ K, both$\kappa_{xx}$ and $\kappa_{xy}$ exhibit distinct anomalies (kinks) at the uppercritical field $H_{c2}$ and at a field $H^*$ slightly below $H_{c2}$. Theanalysis of the thermal Hall angle ($\kappa_{xy}/\kappa_{xx}$) indicates achange of the quasiparticle scattering rate at $H^*$. These results providestrong support to the previous suggestion that above $H^*$ a distinctfield-induced superconducting phase emerges with an unprecedented large spinimbalance.

Quasiparticle Excitations in the Superconducting State of FeSe Probed by Thermal Hall Conductivity in the Vicinity of the BCS-BEC Crossover