We investigate localization and topological properties of a dimerized Kitaev chain with p-wave superconducting correlations and a quasiperiodically modulated chemical potential. With regard to the localization studies, we demonstrate the existence of distinct phases, such as, the extended phase, the critical (intermediate) phase, and the localized phase that arise due to the competition between the dimerization and the onsite quasiperiodic potential. Most interestingly, the critical phase comprises of two different mobility edges that are found to exist between the extended to the localized phase, and between the critical (multifractal) and localized phases. We perform our analysis employing the inverse and the normalized participation ratios, fractal dimension, and the level spacing. Subsequently, a finite-size analysis is done to provide support of our findings. Furthermore, we study the topological properties of the zero-energy edge modes via computing the real-space winding number and number of the Majorana zero modes present in the system. We specifically illustrate that our model exhibits a phase transition from a topologically trivial to a non-trivial phase (topological Anderson phase) beyond a critical dimerization strength under the influence of the quasiperiodic potential strength. Finally, in presence of a large potential, we demonstrate that the system undergoes yet another transition from the topologically non-trivial to an Anderson localized phase. Thus, we believe that our results will aid exploration of fundamentally different physics pertaining to the critical and the topological Anderson phases.

中文翻译：

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存在准周期势的二聚基塔耶夫链的临界和拓扑相

我们研究了具有 p 波超导相关性和准周期调制化学势的二聚化 Kitaev 链的定位和拓扑特性。关于局部化研究，我们证明了由于二聚化和现场准周期电位之间的竞争而产生的不同相的存在，例如扩展相、临界（中间）相和局部相。最有趣的是，临界相包含两个不同的迁移率边缘，发现它们存在于扩展相到局部相之间，以及临界相（多重分形）和局部相之间。我们使用逆和归一化参与比、分形维数和水平间距进行分析。随后，进行有限尺寸分析以支持我们的研究结果。此外，我们通过计算系统中存在的实空间绕组数和马约拉纳零模式的数量来研究零能量边缘模式的拓扑特性。我们特别说明了我们的模型在准周期势强度的影响下表现出从拓扑微不足道到非微不足道相（拓扑安德森相）的相变，超出了临界二聚化强度。最后，在存在巨大潜力的情况下，我们证明该系统经历了从拓扑非平凡阶段到安德森局部阶段的又一次转变。因此，我们相信我们的结果将有助于探索与临界和拓扑安德森相有关的根本不同的物理学。我们通过计算系统中存在的马约拉纳零模式的实空间绕组数和数量来研究零能量边缘模式的拓扑特性。我们特别说明了我们的模型在准周期势强度的影响下表现出从拓扑微不足道到非微不足道相（拓扑安德森相）的相变，超出了临界二聚化强度。最后，在存在巨大潜力的情况下，我们证明该系统经历了从拓扑非平凡阶段到安德森局部阶段的又一次转变。因此，我们相信我们的结果将有助于探索与临界和拓扑安德森相有关的根本不同的物理学。我们通过计算系统中存在的马约拉纳零模式的实空间绕组数和数量来研究零能量边缘模式的拓扑特性。我们特别说明了我们的模型在准周期势强度的影响下表现出从拓扑微不足道到非微不足道相（拓扑安德森相）的相变，超出了临界二聚化强度。最后，在存在巨大潜力的情况下，我们证明该系统经历了从拓扑非平凡阶段到安德森局部阶段的又一次转变。因此，我们相信我们的结果将有助于探索与临界和拓扑安德森相有关的根本不同的物理学。