Electromagnetic responses based on quantum geometry in semiconductors and superconductors

Many dielectric and optical responses in semiconductors, including charge susceptibility, relative dielectric constant, optical conductivity, dielectric function, refractive index, absorption coefficient, reflectance, and transmittance, will be shown to be originated from the quantum geometry of valence band state, allowing to experimentally measure the so-called spread of Wannier functions that has been intensively discussed in density functional theory. The quantum metric itself can be detected by pump-probe measurements combined with time-resolved ARPES, and the same kind of experiment can also detect Berry curvature and spin Berry curvature. In a similar fashion, the quasihole states of conventional superconductors also possess a quantum metric that determines the infrared absorption, paramagnetic current, and dielectric response. Remarkably, the Meissner effect is also determined by quantum geometry, and this recognition introduces a superfluid weight marker to investigate the local diamagnetic current under the influence of disorder, as well as a superfluid weight correlator that describes the nonlocal electromagnetic responses beyond the phenomenological theory of Pippard.