论文标题
拓扑绝缘子和向量捆绑包的几何形状
Topological insulators and geometry of vector bundles
论文作者
论文摘要
长期以来，固体的带理论一直集中在能量谱或哈密顿特征值上。最近，人们意识到特征向量的收集还包含重要的物理信息。特征空间的局部几何形状决定了电化极化，而它们的全局扭曲产生了拓扑绝缘体中的金属表面状态。这些现象是当前注释的中心主题。特征空间的形状还负责许多有趣的物理类比，它们的根源在矢量束理论中。我们对矢量束的几何形状和拓扑进行了非正式介绍，并从这个数学角度描述了各种物理模型。
For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of eigenspaces determines the electric polarization, while their global twisting gives rise to the metallic surface states in topological insulators. These phenomena are central topics of the present notes. The shape of eigenspaces is also responsible for many intriguing physical analogies, which have their roots in the theory of vector bundles. We give an informal introduction to the geometry and topology of vector bundles and describe various physical models from this mathematical perspective.
