AI 中文总结
研究轴子拓扑材料在电磁场下的响应，采用基于表面变量的技术，通过边界有限元法求解积分方程，对不同几何形状的拓扑绝缘体进行数值模拟，证明变分原理可恢复表面变量方程。
AI 中文摘要
我们研究了轴子拓扑材料在外部静电力和磁场存在下的响应。我们专注于拓扑绝缘体的宏观准静态磁电响应。我们使用基于表面变量的技术，该技术先前已用于软凝聚态物质问题，以描述由多种均匀材料组成的异质系统。整个系统的完整描述是根据表面自由度编写的，在这种情况下，表面自由度对应于有效表面电荷和表面电流密度。我们得到了这些变量满足的一组积分方程。我们给出了轴对称情况的精确解析解。我们通过边界有限元方法开发了一种求解积分方程的数值方法。我们将该数值方法应用于具有不同几何形状的拓扑绝缘体，如球体、空心球体和环形表面。我们表明变分原理可用于恢复表面变量方程。
英文摘要
We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.
