  Recently, non-reciprocal two-dimensional unitary scattering networks have
gained considerable interest due to the possibility of obtaining robust edge
wave propagation in the anomalous Floquet phase. Conversely, zero-dimensional
topological states in such networks have been left uncharted. Here, we
demonstrate the existence of Floquet disclination states in non-reciprocal
scattering networks. The disclination states, characterized by spectral
charges, nucleate in the anomalous phase from a resonant rotation-symmetric
phase matching condition, and survive until the bandgaps close. Once coupled to
the radiation continuum feeding the anomalous chiral edge state, they can
induce intriguing topological disclination bound states in the continuum
(BICs), associated with an extreme confinement and lifetime. Altogether,
anomalous Floquet disclination states and topological disclination BIC broaden
the applications of disclination states to microwave, acoustic or optical
scattering networks, with new possibilities in chiral topological lasing,
robust energy squeezing from topological bound states, and switchable lasing
and anti-lasing behavior induced via unidirectional topological coupling.
