Dielectric and optical markers originating from quantum geometry

Abstract

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.