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For decades, the topological phenomena in quantum systems have always beencatching our attention. Recently, there are many interests on the systems wheretopologically protected edge states exist, even in the presence ofnon-Hermiticity. Motivated by these researches, the topological properties of anon-Hermitian dice model are studied in two non-Hermitian cases, viz. in theimbalanced and the balanced dissipations. Our results suggest that thetopological phases are protected by the real gaps and the bulk-edgecorrespondence readily seen in the real edge-state spectra. Besides, we showthat the principle of the bulk-edge correspondence in Hermitian case is stilleffective in analyzing the three-band non-Hermitian system. We find that thereare topological non-trivial phases with large Chern numbers $C=-3$ robustagainst the dissipative perturbations.

Large Chern numbers in a dissipative dice model