  Generally, the topological corner state in two-dimensional second-order
topological insulator (2D SOTI) is equivalent to the well-known domain wall
state, originated from the mass-inversion between two adjacent edges with phase
shift of pi. In this work, go beyond this conventional physical picture, we
report a fractional mass-kink induced 2D SOTI in monolayer FeSe with canted
checkerboard antiferromagnetic (AFM) order by analytic model and
first-principles calculations. The canted spin associated in-plane Zeeman field
can gap out the quantum spin Hall edge state of FeSe, forming a fractional
mass-kink with phase shift of pi/2 at the rectangular corner, and generating an
in-gap topological corner state with fractional charge of e/4. Moreover, the
topological corner state is robust to local perturbation, existing in both
naturally and non-naturally cleaved corners, regardless of the edge
orientation. Our results not only demonstrate a material system to realize the
unique 2D AFM SOTI, but also pave a new way to design the higher-order
topological states from fractional mass-kink with arbitrary phase shift, which
are expected to draw immediate experimental attention.
