论文标题
量化表面磁性和高阶拓扑：应用于HOPF绝缘体
Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
论文作者
论文摘要
我们确定了三维结晶石的表面贡献的巨大磁矩的拓扑方面 - 假定在整体和所有表面方面都在绝缘，并且散装中有琐碎的Chern不变性。这种延伸力矩的几何成分是由其在零温度和零场的化学电位相对于每个单位表面积下的化学电位给出的，因此对应于表面磁性可压缩性。由立方体晶体的两个相对方面贡献的表面压缩性的总和被量化为基本常数$ e/h c $的整数倍数；该整数与铰链模式的净手性在一对一的对应关系中，表现为具有高阶拓扑的链接。单个方面对磁压缩性的贡献不必对整数进行量化；但是，对称和/或希尔伯特空间约束可以将单法压缩性固定到$ e/hc $的半耗时性倍数上，这将由Hopf Instrulator示例。
We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite -- assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is quantized to an integer multiple of the fundamental constant $e/h c$; this integer is in one-to-one correspondence with the net chirality of hinge modes on the surface of the crystallite, manifesting a link with higher-order topology. The contribution by a single facet to the magnetic compressibility need not be quantized to integers; however, symmetry and/or Hilbert-space constraints can fix the single-facet compressibility to half-integer multiples of $e/hc$, as will be exemplified by the Hopf insulator.
