  The dynamical and topological properties of non-Hermitian systems have
attracted great attention in recent years. In this work, we establish an
intrinsic connection between two classes of intriguing phenomena -- topological
phases and dynamical quantum phase transitions (DQPTs) -- in non-Hermitian
systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs
following the quench from a trivial to a non-Hermitian topological phase.
Moreover, the number of critical momenta and critical time periods of the DQPTs
are found to be directly related to the topological invariants of the
non-Hermitian system. We further demonstrate our theory in three prototypical
non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with
next-nearest-neighbor hoppings, and the nonreciprocal Su-Schrieffer-Heeger
model. Finally, we present a proposal to experimentally verify the found
connection by a nitrogen-vacancy center in diamond.
