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 electric field. While the static electrical conductivity is vanishingly small in insulators, the optical conductivity always remains finite in some frequency intervals ; 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, these properties can be considered as scalar functions of the frequency only. Then, the electric current density , the scalar optical conductivity and the electric field vector are linked by the equation
while the dielectric function relates the electrical displacement to the electric field:
In SI units, this implies the following connection between the two linear response functions:
where is the vacuum permittivity and denotes the imaginary unit.
The optical conductivity is most often measured in the optical frequency ranges via the reflectivity of polished samples under normal incidence or using variable incidence angles. For samples that can be prepared in thin slices, higher precision is usually obtainable using optical transmission experiments. In order to get more complete information about the electronic properties of the material of interest, such measurements have to be combined with other techniques that work in remaining frequency ranges, e.g., in the static limit or at microwave frequencies.
