We study non-Hermitian Aubry-André-Harper models with $p$-wave pairing, where the non-Hermiticity is introduced by on-site complex quasiperiodic potentials. By analyzing the $\mathcal{PT}$ symmetry breaking, winding numbers of energy spectra, localization and fractal dimensions of states, and fate of Majorana fermions, a complete phase diagram on localization and topological phase transitions is obtained. In particular, the non-Hermitian topological nature of localization phase transitions from extended to critical and then to localized phases is identified, using both analytical and numerical methods. In the critical phase, the complex spectrum is topologically nontrivial with a fractional winding number. In the localized phase the analytical localization length of states can apply to the Hermitian case, which is absent so far. Both the non-Hermiticity and quasiperiodicity are detrimental to Majorana fermions.

中文翻译：

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具有 p 波配对的非 Hermitian Aubry-André-Harper 模型中的定位和拓扑相变

我们研究了非 Hermitian Aubry-André-Harper 模型 $磷$波配对，其中非厄米性是由现场复杂的准周期势引入的。通过分析$\mathcal{PT}$根据对称性破缺、能谱缠绕数、状态的定域和分形维数以及马约拉纳费米子的命运，获得了关于定域和拓扑相变的完整相图。特别是，使用解析和数值方法识别了从扩展相到临界相再到局部化相的局部化相变的非厄米拓扑性质。在临界阶段，复谱在拓扑上是非平凡的，具有分数绕组数。在局部化阶段，状态的解析局部化长度可以应用于 Hermitian 情况，目前尚不存在这种情况。非厄米性和准周期性都对马约拉纳费米子有害。