标题： 无中心对称杂质超导体中的局域化与拓扑性 显示英文标题

标题： Localization and Topology in Noncentrosymmetric Superconductors with Disorder

摘要： 著名的Kitaev链在存在各种无序的情况下展现出引人入胜的相图，包括多分形态和拓扑安德森相。 在本工作中，我们研究了在准周期性和安德森无序下，二聚化拓扑非中心对称超导体（NCS）的局域化和拓扑性质。 通过全局和局部表征方法，我们识别出从遍历态到多分形态和局域态的能量依赖性转变。 扩展的多分形区域来源于二聚化、NCS序和准周期调制之间的竞争。 这种相互作用导致局域化在不同的能带中优先发生，取决于无序强度，最低能带对参数变化表现出最高的敏感性。 我们采用实空间极化方法计算$\mathbb{Z}_2$拓扑不变量，揭示了随着准周期势的增加，拓扑相和平凡相交替出现，这种行为与典型的拓扑安德森相图不同。 此外，拓扑态对安德森无序表现出显著的鲁棒性，为非中心对称系统中的拓扑相稳定性提供了新的见解。 最后，我们提出了一种基于超导约瑟夫森结的可行实验方案，在该方案中，可以通过空间调制的超电流实现类似NCS的行为。 我们的发现突显了不同无序类型在塑造局域化和拓扑性中的独特作用，为马约拉纳零模的工程化提供了洞察，并对拓扑量子加密方案具有深远的意义。 显示英文摘要

摘要： The celebrated Kitaev chain reveals a captivating phase diagram in the presence of various disorders, encompassing multifractal states and topological Anderson phases. In this work, we investigate the localization and topological properties of a dimerized topological noncentrosymmetric superconductor (NCS) under quasiperiodic and Anderson disorders. Using both global and local characterization methods, we identify energy-dependent transitions from ergodic to multifractal and localized states. Extended multifractal regimes emerge from the competition between dimerization, NCS order, and quasiperiodic modulation. This interplay causes localization to occur preferentially in different energy bands depending on the disorder strength, with the lowest bands exhibiting the highest sensitivity to parameter variations. We employ the real-space polarization method to compute the $\mathbb{Z}_2$ topological invariant, revealing alternating topological and trivial phases as the quasiperiodic potential increases, a behavior distinct from the typical topological Anderson phase diagram. Additionally, the topological states show remarkable robustness against Anderson disorder, providing new insights into topological phase stability in non-centrosymmetric systems. Finally, we propose a feasible experimental scheme based on superconducting Josephson junctions, where NCS-like behavior can be engineered via spatially modulated supercurrents. Our findings highlight the distinct roles of different disorder types in shaping localization and topology, providing insight into the engineering of Majorana zero modes and offering profound implications for topological quantum encryption schemes.