拓扑绝缘体的连续体块体与界面描述
Continuous bulk and interface description of topological insulators
AI总结：
该研究分析狄拉克方程组形式的拓扑绝缘体连续模型，利用Fredholm算子指标描述体块与界面拓扑性质并证明其对空间异质性扰动的稳定性，先针对二维材料提出后推广到任意维度，为拓扑与空间涨落相互作用分析提供定量工具。
摘要：
我们分析了狄拉克方程组形式的拓扑绝缘体连续偏微分模型。通过谱演算从狄拉克算子构造Fredholm算子，利用其指标描述材料的体块和界面拓扑性质。我们证明这些拓扑不变量对大类空间异质性扰动的稳定性。这些模型为分析物质拓扑相中的拓扑与空间涨落相互作用提供定量工具。该理论首先针对二维材料提出，此类材料沿界面表现出不对称（手性）输运；随后推广到任意维度，奇数空间维度需额外假设手性对称性。
英文摘要：
We analyze continuous partial differential models of topological insulators in the form of systems of Dirac equations. We describe the bulk and interface topological properties of the materials by means of indices of Fredholm operators constructed from the Dirac operators by spectral calculus. We show the stability of these topological invariants with respect to perturbations by a large class of spatial heterogeneities. These models offer a quantitative tool to analyze the interplay between topology and spatial fluctuations in topological phases of matter. The theory is first presented for two-dimensional materials, which display asymmetric (chiral) transport along interfaces. It is then generalized to arbitrary dimensions with the additional assumption of chiral symmetry in odd spatial dimensions.
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