Topological phases are greatly enriched by including non-Hermiticity. While most works focus on the topology of the eigenvalues and eigenstates, how topologically nontrivial non-Hermitian systems behave in dynamics has only drawn limited attention. Here, we consider a breathing honeycomb lattice known to emulate the quantum spin Hall effect and exhibit higher-order corner modes. We find that nonreciprocal intracell couplings introduce gain in one pseudospin subspace while introducing loss with the same magnitude in the other. In addition, nonreciprocal intracell couplings can also suppress the spin mixture of the edge modes at the boundaries and delocalize the higher-order corner mode. Our findings deepen the understanding of non-Hermitian topological phases and bring in the spin degree of freedom in manipulating the dynamics in non-Hermitian systems.

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• Topological effects in photonic systems
• Topological insulators
• Non-Hermitian systems