  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper
pairs condensed at finite momentum, has been a long-sought state that remains
unresolved in many classes of fermionic systems, including superconductors and
ultracold atoms. A fascinating aspect of the FFLO state is the emergence of
periodic nodal planes in real space, but its observation is still lacking. Here
we investigate the superconducting order parameter at high magnetic fields $H$
applied perpendicular to the $ab$ plane in a high-purity single crystal of
FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for
a distinct superconducting phase at the low-temperature/high-field corner of
the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging
scanning tunneling microscopy performed on the same crystal demonstrates that
the order parameter vanishes at the surface upon entering the high-field phase.
These results provide the first demonstration of a pinned planar node
perpendicular to $H$, which is consistent with a putative FFLO state.
