We study bulk-boundary correspondences and related surface phenomenastabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis using operator algebraic methods. We use the connecting maps between the K -theories of bulk and boundary algebras as engines for the bulk-boundary correspondences. We discovered that both the exponential and the index connecting maps are relevant for the context considered here as they lead to distinct experimentally observable surface phenomena, such as pumping and transfer of quantum surface Hall states or proximity induced Hall effect. The surface Hall physics of time-reversal symmetric topological insulators is also investigated using the new tools, which can model irrational magnetic fluxes and arbitrary large surface disorder.

中文翻译：

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具有定量磁电效应的拓扑绝缘子的体边界对应

我们研究了绝热循环驱动的三维绝缘子中由第二切恩数稳定的体边界对应关系和相关表面现象。使用算子代数方法将磁场和无序效应纳入我们的分析。我们使用块体和边界代数的K理论之间的连接图作为块体-边界对应关系的引擎。我们发现指数连接图和索引连接图都与此处考虑的上下文相关，因为它们会导致不同的实验可观察表面现象，例如量子表面霍尔状态的泵浦和转移或邻近感应霍尔效应。还使用新工具研究了时间反向对称拓扑绝缘子的表面霍尔物理，