发表机构
Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出实空间景观方法，通过将零能方程转化为一阶动力学系统，以稳定轨迹识别马约拉纳零模，并给出非均匀性振幅与梯度的充分界限，为器件设计提供定量标准。
AI 中文摘要
空间非均匀性破坏了平移对称性，并阻止了常规布洛赫带拓扑不变量直接回答一个实际问题：马约拉纳零模是否能在给定的非均匀超导器件中存活？在本文中，我们发展了一种实空间景观方法来解决这个问题。我们不将零能方程作为边值问题求解，而是将空间坐标视为演化参数，并将该方程重新表述为一阶动力学系统。马约拉纳零模随后被识别为满足物理边界条件并在大距离处趋近原点的稳定轨迹。我们表明，景观几何固定了稳定和不稳定子空间的维度，而稳定子空间与物理边界子空间的交集决定了马约拉纳零模的数量。在均匀极限下，拓扑相变表现为景观的几何转变。将该方法应用于一维无自旋p波超导体和纳米线-超导体系统，该方法对非均匀性的振幅和空间梯度都给出了充分界限，为马约拉纳器件的设计提供了定量标准。
英文摘要
Spatial inhomogeneity breaks translational symmetry and prevents conventional Bloch-band topological invariants from directly answering a practical question: do Majorana zero modes survive in a given inhomogeneous superconducting device? In this Letter, we develop a real-space landscape approach to address this question. Rather than solving the zero-energy equation as a boundary-value problem, we treat the spatial coordinate as an evolution parameter and recast the equation as a first-order dynamical system. A Majorana zero mode is then identified with a stable trajectory that satisfies the physical boundary condition and approaches the origin at large distance. We show that the landscape geometry fixes the dimensions of the stable and unstable subspaces, while the intersection of the stable subspace with the physical boundary subspace determines the number of Majorana zero modes. In the homogeneous limit, the topological phase transition is manifested as a geometric transition of the landscape. Applied to one-dimensional spinless $p$-wave superconductors and nanowire--superconductor systems, the approach yields sufficient bounds on both the amplitude and spatial gradient of the inhomogeneity, providing quantitative criteria for the design of Majorana devices.
