  We study the quench dynamics of non-Hermitian topological models with
non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting
quench dynamics onto the generalized Brillouin zone, we find that emergent
topological structures, in the form of dynamic skyrmions, exist in the
generalized momentum-time domain, and are correlated with the non-Bloch
topological invariants of the static Hamiltonians. The skyrmion structures
anchor on the fixed points of dynamics whose existence are conditional on the
coincidence of generalized Brillouin zones of the pre- and post-quench
Hamiltonians. Global signatures of dynamic skyrmions, however, persist well
beyond such a condition, thus offering a general dynamic detection scheme for
non-Bloch topology in the presence of non-Hermitian skin effects. Applying our
theory to an experimentally relevant, non-unitary quantum walk, we explicitly
demonstrate how the non-Bloch topological invariants can be revealed through
the non-Bloch quench dynamics.
