arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2203.00484cond-mat.mes-hall
收藏

基于物理图的机器学习识别二阶非厄米趋肤效应

Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning

Ce Shang, Shuo Liu, Ruiwen Shao, Peng Han, Xiaoning Zang, Xiangliang Zhang, Khaled Nabil Salama, Wenlong Gao, Ching Hua Lee, Ronny Thomale, Aurelien Manchon, Sh… 展开作者

Ce Shang, Shuo Liu, Ruiwen Shao, Peng Han, Xiaoning Zang, Xiangliang Zhang, Khaled Nabil Salama, Wenlong Gao, Ching Hua Lee, Ronny Thomale, Aurelien Manchon, Shuang Zhang, Tie Jun Cui, Udo Schwingenschlogl

摘要:

物质的拓扑相通常由埃尔米特系统中的体-边界对应来表征:$d$维度中的体的拓扑不变量对应于$(d-1)$维边界状态的数量。通过扩展,高阶拓扑绝缘体揭示了体-边-角对应,使得$n$阶拓扑相具有$(d-n)$维边界态。非厄米拓扑系统的出现为在开边界条件下具有大量边界模的非厄米趋肤效应(NHSE)的出现提供了新的线索。尽管如此,高阶NHSE仍然在很大程度上未被探索,特别是在实验中。我们引入了一种无监督的方法-物理图通知机器学习(PGIML)-以提高机器学习的数据挖掘能力与有限的领域知识。通过PGIML,我们在一个二维非厄米拓扑电路中实验证明了二阶NHSE。该电路的导纳谱表现出大量的角落皮肤模式和极端的灵敏度的频谱流的边界条件。在二阶NHSE中违反了传统的体边界对应,这意味着在高维非厄米系统中拓扑带理论的修改是不可避免的。

英文摘要:

Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that $n$-th order topological phases feature $(d-n)$-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. We introduce an unsupervised approach -- physics-graph-informed machine learning (PGIML) -- to enhance the data mining ability of machine learning with limited domain knowledge. Through PGIML, we experimentally demonstrate the second-order NHSE in a two-dimensional non-Hermitian topolectrical circuit. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑