  In the creation of Hopf topological matters, the old paradigm is to conceive
the Hopf invariant first, and then display its intuitive topology through
links. Here we brush aside this effort and put forward a new recipe for
unraveling the quenched two-dimensional (2D) two-band Chern insulators under a
parallel quench protocol, which implies that the quench quantities with
different momentum k are parallel or antiparallel to each other. We find that
whether the dynamical Hopf invariant exists or not, the links in (2+1)D space
always keep their standard shape even for topological initial states, and trace
out the trajectories of phase vortices. The linking number is exactly equal to
the difference between pre- and post-quench Chern numbers regardless of the
construction of homotopy groups. We employ two concrete examples to illustrate
these results, highlighting the polarity reversal at fixed points.
