  Typical BCS superconductors are microscopically homogeneous in real space
governed by the coherent Cooper pairs with high phase stiffness of superfluid
density, which is characterized by a coherence length. However, a periodic
oscillation of superconducting order parameter may develop driven by breaking
the time-reversal or translational invariance. To date, such modulated orders
were specific to each material systems, with a periodicity much larger than the
lattice constant. Here we report the direct observation of a uniform
lattice-scale pair density wave (PDW) in single-layer FeSe/SrTiO3 films,
enforced by peculiar interfacial structure of crystal symmetries breaking. Our
spectroscopic imaging scanning tunneling microscopy unravels a spatial
modulation of Cooper-pairing gap within a single unit-cell, depending on
inequivalent atomic sites. Prominent periodic variation of superfluid density
is visualized via Josephson current by a superconducting tip, indicating a
real-space oscillation of phase stiffness. Such a lattice-scale superconducting
modulation, which coexists with a larger length scale of PDW order, indicates
the lattice-scale variation of both pairing strength and phase stiffness. Our
findings provide new insights into the intertwined density-wave orders of
quasiparticle character in correlated electronic systems, and provoke future
studies on the unconventional pairing interaction and phase stiffness in the
two-dimensional limit.
