We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of ground states occurs, associated with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist in an open chain in the time-reversal symmetry-unbroken region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.

中文翻译：

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具有不平衡配对的Kitaev链中的拓扑阶段

我们系统地研究了具有非平衡对创建和an灭的Kitaev链，该链由非Hermitian配对项引入。精确的相位图表明，在条件不平衡的影响下，拓扑相位仍然很健壮。带隙相的特征在于拓扑不变性，即扩展的Zak相，其由生物正交的内积定义。在发生基态合并的点处破坏了这些相位，这与时间反转对称性破裂相关。我们发现，Majorana边缘模式也存在于时间反转对称不间断区域的开放链中，这说明了在这种非Hermitian系统中的体边缘对应关系。