We unveil a peculiar dynamical transition for the propagation of wave packets in non-Hermitian Chern insulators, where the evolution of the topological wave packets at the edge is not determined solely by the topological Chern number. Unlike the Hermitian Chern insulator, where a wave packet initiated at the edge propagates along the system boundary, here, it may instead penetrate into the bulk. This behavior is attributed to the competition between the localization induced by conventional topology and the non-Hermitian skin effect. Specifically, when the former dominates, the wave packet will evolve along the boundary; otherwise, it will spread into the bulk. These features demonstrate that while the generalized-Brillouin-zone framework reliably predicts topological phase transitions, it does not on its own specify the dynamical transitions.

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• Anomalous Hall effect
• Dynamical phase transitions
• Edge states
• Phase separation
• Non-Hermitian systems