We introduce a one-dimensional non-Hermitian Kitaev chain with staggered imbalance in the $p$-wave superconducting pairing. By tuning the chemical potential and the pairing imbalance, we find that the eigenenergy spectrum undergoes real-to-complex transitions, and the spectral gap can change from a real line gap to an imaginary one. The pairing imbalance significantly enlarges the parameter region supporting a topological superconducting phase. Remarkably, we show that a topologically nontrivial phase hosting Majorana zero modes can be induced by varying the pairing imbalance, even in the regime of strong chemical potential. The gap-closing points and phase boundaries are determined analytically, and the resulting phase diagrams are presented with the nontrivial phase characterized by a nonzero topological invariant. Furthermore, we identify the coexistence of Majorana zero modes and finite-energy Majorana edge modes in this system. Our results reveal exotic phenomena arising from imbalanced pairing and establish a platform for exploring topological superconductivity in non-Hermitian systems.

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• Topological superconductors
• 1-dimensional systems
• Non-Hermitian systems