  The de Gennes extrapolation length is a direction dependent measure of the
spatial evolution of the pairing gap near the boundary of a superconductor, and
thus provides a viable means to probe its symmetry. It is expected to be
infinite and isotropic for plain s-wave pairing, and finite and anisotropic for
d-wave. Here, we synthesize single layer FeSe films on SrTiO3(001) (STO)
substrates by molecular beam epitaxy, and measure the de Gennes extrapolation
length by scanning tunneling microscopy/spectroscopy. We find a 40% reduction
of the superconducting gap near specular [110]Fe edges, yielding an
extrapolation length of 8.0 nm. However, near specular [010]Fe edges the
extrapolation length is nearly infinite. These findings are consistent with a
phase changing pairing with 2-fold symmetry, indicating d-wave
superconductivity. This is further supported by the presence of in-gap states
near the specular [110]Fe edges, but not the [010]Fe edges. This work provides
direct experimental evidence for d-wave superconductivity in single layer
FeSe/STO, and demonstrates quasiparticle scattering at boundaries to be a
viable phase sensitive probe of pairing symmetry in Fe-based superconductors.
