源自量子几何的介电与光学标记
Dielectric and optical markers originating from quantum geometry
AI总结：
本文证明半导体与绝缘体的多种非激子介电和光学性质源于量子几何，并提出可映射到实空间晶格位点的局域标记，以解释近场光学观测的空间不均匀性及探测保真度标记。
摘要：
我们详细阐明，半导体和绝缘体中由带间吸收引起的许多非激子介电与光学性质均起源于量子几何，包括电荷极化率、相对介电常数、光电导率、介电函数、折射率、吸收系数、反射率和透射率。形成这一认识的关键在于复光电导率：其光学跃迁矩阵元中包含量子度规，而且所有这些介电与光学性质都可以用光电导率的实部和虚部来表示。我们的形式体系能够将所有这些性质映射为实空间晶格位点上的局域标记，这有助于解释近场扫描光学显微镜所探测到的光学性质空间不均匀性；一个三维拓扑绝缘体的最小模型对此进行了演示。此外，介电函数标记可用于探测最近提出的保真度标记，或者等价地，用于探测推广至无序绝缘体的价带 Wannier 函数的展宽。
英文摘要：
We elaborate that many non-excitonic dielectric and optical properties of semiconductors and insulators caused by interband absorption are originated from quantum geometry, including charge susceptibility, relative dielectric constant, optical conductivity, dielectric function, refractive index, absorption coefficient, reflectance, and transmittance. The key to this recognition is the complex optical conductivity, which contains the quantum metric in the optical transition matrix element, and the fact that all these dielectric and optical properties can be expressed in terms of the real and imaginary parts of optical conductivity. Our formalism allows to map all these properties to real space lattice sites as local markers, which can help to explain the spatial inhomogeneity of optical properties detected by near-field scanning optical microscopy, as demonstrated by a minimal model of 3D topological insulators. In addition, the dielectric function marker can be used to detect a recently proposed fidelity marker, or equivalently the spread of valence-band Wannier functions generalized to disordered insulators.
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