  In condensed-matter physics spin-orbit coupling (SOC) is a fundamental
physical interaction, which describes how the electrons' spin couples to their
orbital motion. It is the source of a vast variety of fascinating phenomena in
solids such as topological phases of matter, quantum spin Hall states, and many
other exotic quantum states. Although in most theoretical descriptions of the
phenomenon of high-temperature superconductivity SOC has been neglected,
including this interaction can, in principle, revise the microscopic picture of
superconductivity in these compounds. Not only the interaction leading to
Cooper pairing but also the symmetry of the order parameter and the topological
character of the involved states can be determined by SOC. Here by preforming
energy-, momentum-, and spin-resolved spectroscopy experiments with an
unprecedented resolution we demonstrate that while probing the dynamic charge
response of the FeSe monolayer on strontium titanate, a prototype two
dimensional high-temperature superconductor using slow electrons, the
scattering cross-section shows a considerable spin asymmetry. We unravel the
origin of the observed spin asymmetry by developing a model in which SOC is
taken into consideration. Our analysis indicates that SOC in this two
dimensional superconductor is rather strong. We anticipate that such a strong
SOC can have several serious consequences on the electronic structures and can
lead to the formation of topological states. Moreover, a sizable SOC can
compete with other pairing scenarios and is crucial for the mechanism of
high-temperature superconductivity.
