  Three-dimensional (3D) topological materials exhibit much richer phenomena
than their lower-dimensional counterparts. Here, we propose self-localized
topological states (i.e., topological solitons) in a 3D nonlinear photonic
Chern insulator. Despite being in the bulk and self-localized in all 3D, the
topological solitons at high-symmetry points K and K' rotate in the same
direction, due to the underlying topology. Specifically, under the saturable
nonlinearity the solitons are stable over a broad frequency range. Our results
highlight how topology and nonlinearity interact with each other and can be
extended to other 3D topological systems.
