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Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry

We propose a non-Hermitian topological system protected by the generalized rotational symmetry which invokes rotation in space and Hermitian conjugation. The system, described by the tight-binding model with nonreciprocal hopping, is found to host two pairs of in-gap edge modes in the gapped topological phase and is characterized by the non-Hermitian (NH) Chern number $C_{NH}=2$. The quantization of the non-Hermitian Chern number is shown to be protected by the generalized rotational symmetry $Ĥ^{+}=ÛĤÛ^{+}$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants and hosting multiple in-gap edge states, which can be used for topologically resilient multiplexing.