Large Chern numbers in a dissipative dice model

For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity. Motivated by these researches, the topological properties of a non-Hermitian dice model are studied in two non-Hermitian cases, viz. in the imbalanced and the balanced dissipations. Our results suggest that the topological phases are protected by the real gaps and the bulk-edge correspondence readily seen in the real edge-state spectra. Besides, we show that the principle of the bulk-edge correspondence in Hermitian case is still effective in analyzing the three-band non-Hermitian system. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.