标题： 通过均质化理论的拓扑安德森绝缘体 显示英文标题

标题： Topological Anderson Insulators by homogenization theory

摘要： (陈)拓扑绝缘体的一个核心特性是，在不同拓扑相的二维绝缘材料之间的界面处存在稳健的不对称输运。 拓扑安德森绝缘体是一种其拓扑相由空间涨落引起的绝缘体。 本文提出了一种受扰狄拉克方程的数学模型，并表明对于足够大且高度振荡的扰动，系统处于与未受扰模型不同的拓扑相。 特别是，在受扰和未受扰相之间的界面处确实出现了稳健的不对称输运。 理论结果基于狄拉克方程均质化理论中预解算子的细致估计，以及通过适当弗雷德霍姆算子的指标对拓扑相的表征。 显示英文摘要

摘要： A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in different topological phases. A Topological Anderson Insulator is an insulator whose topological phase is induced by spatial fluctuations. This paper proposes a mathematical model of perturbed Dirac equations and shows that for sufficiently large and highly oscillatory perturbations, the systems is in a different topological phase than the unperturbed model. In particular, a robust asymmetric transport indeed appears at an interface separating perturbed and unperturbed phases. The theoretical results are based on careful estimates of resolvent operators in the homogenization theory of Dirac equations and on the characterization of topological phases by the index of an appropriate Fredholm operator.