标题： 序贯拓扑：有限手性结构中的迭代拓扑相变 显示英文标题

标题： Sequential topology: iterative topological phase transitions in finite chiral structures

摘要： 我们提出了理论和实验结果，探讨了具有手征对称性的任意无序有限紧束缚哈密顿量的丰富拓扑结构。我们通过考虑相边界本身的拓扑性质来扩展已知分类。也就是说，那些局限于拓扑边缘状态的哈密顿量是否也可以具有不同的拓扑相？对于手征结构，我们对此问题给出了肯定的回答，在这里我们将拓扑相边界定义为实空间零模式的不可避增加的简并度。通过迭代这一问题，并考虑如何将哈密顿量限制到相边界，我们给出了一种协议，以找到具有特定零能态简并度的最大维度子空间，我们将其称为\textit{序列拓扑}。我们展示了这种简并度会改变零模式的局域化和输运性质，使我们能够使用最先进的同轴电缆平台实验性地验证我们的理论。我们的理论适用于具有任意基础连通性或无序性的系统，因此可以计算任何有限的手征结构。讨论了我们工作的技术和理论应用。 显示英文摘要

摘要： We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological properties of phase boundaries themselves. That is, can Hamiltonians that are confined to being topologically marginal, also have distinct topological phases? For chiral structures, we answer this in the affirmative, where we define topological phase boundaries as having an unavoidable increase in the degeneracy of real space zero modes. By iterating this question, and considering how to enforce a Hamiltonian to a phase boundary, we give a protocol to find the largest dimension subspace of a disordered parameter space that has a certain order degeneracy of zero energy states, which we call \textit{sequential topology}. We show such degeneracy alters localisation and transport properties of zero modes, allowing us to experimentally corroborate our theory using a state-of-the-art coaxial cable platform. Our theory applies to systems with an arbitrary underlying connectivity or disorder, and so can be calculated for any finite chiral structure. Technological and theoretical applications of our work are discussed.