Optical conductivity

The optical conductivity is a material property, which links the current density to the electric field for general frequencies. In this sense, this linear response function is a generalization of the electrical conductivity, which is usually considered in the static limit, i.e., for a time-independent (or sufficiently slowly varying) electric field. While the static electrical conductivity is vanishingly small in insulators (such as Diamond or Porcelain), the optical conductivity always remains finite in some frequency intervals (above the optical gap in the case of insulators); the total optical weight can be inferred from sum rules. The optical conductivity is closely related to the dielectric function, the generalization of the dielectric constant to arbitrary frequencies.

Only in the simplest case (coarse-graining, long-wavelength limit, cubic symmetry of the material), these properties can be considered as (complex-valued) scalar functions of the frequency only. Then, the electric current density ${\displaystyle \mathbf {J} }$ (a three-dimensional vector), the scalar optical conductivity ${\displaystyle \sigma }$ and the electric field vector ${\displaystyle \mathbf {E} }$ are linked by the equation

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