The topological properties of non-Hermitian systems are quite different from those of their Hermitian counterparts and include defective edge states, breakdown of the bulk-boundary correspondence, and the topological structure of the point gap. Therefore, in non-Hermitian systems, we may use an alternative approach to tune their topological properties. In this work, we present an approach for tuning topological states by inhomogeneous dissipation (or gain/loss). As the dissipation increases, the system evolves from periodic boundary conditions (PBCs) to open boundary conditions (OBCs) at the critical point. A system under closed boundary conditions (CBCs) is torn into two subsystems under OBCs with increasing dissipation. These conclusions can be demonstrated numerically and analytically. During this process, the global phase diagrams are hybrids of those under PBCs and OBCs, and the topological regions are both dissipation tuneable and analytically solvable. Remarkably, various phases and phase transitions appear, and each phase transition corresponds to unique behavioral signatures in the generalized Brillouin zone (GBZ), thus revealing rich GBZ configurations. Additionally, our results can be straightforwardly applied to other non-Hermitian topological states (including higher-dimensional systems) because of their low-energy effective Hamiltonians. Therefore, our work helps researchers better understand non-Hermitian topological systems.

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• Phase diagrams
• Phase transitions
• Topological insulators
• Topological phases of matter
• 1-dimensional systems
• Lattice models in condensed matter
• Su-Schrieffer-Heeger model