  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.
