Optical conductivity is a powerful tool to measure electronic states of materials. Take a material sample. It can be graphene for example.Put it it an electric field. Electronic charges in it get redistributed-polarised in other words. Currents are induced. Fields small? Then induced polarization and currents are proportional to applied field. Experimentally one can measure optical reflectivity and deduce optical conductivity. Let me know if you want more details. CSS

A material is said to be optically conductive, when on falling the light on the material surface, it shows conduction and this phenomena is called optical conductivity. (same as by Sher Zaman).

Optical conductivity is a powerful tool to measure electronic states of materials. Take a material sample. It can be graphene for example.Put it it an electric field. Electronic charges in it get redistributed-polarised in other words. Currents are induced. Fields small? Then induced polarization and currents are proportional to applied field. Experimentally one can measure optical reflectivity and deduce optical conductivity. Let me know if you want more details. CSS

What light or in general an electromagnetic stimulus does to matter is what is measured in optical conductivity. The simple theoretical basis is J = sigma E. And the frequency region could be visible region. Thus the 'tool' is the response itself. And to produce that response we need to apply a stimulus. Photoconductivity is a special case of optical conductivity. Also remember that we need concepts like band structure whereas the Maxwell equation above is quite general. Optical conductivity is a tool in the same sense as Mossbauer spectroscopy is.

I personnally use this term to refer to the conductivity deduced from the analysis of spectra (UV/vis/IR) through *Drude theory. The IR reflectivity above the plasma wavelength is given by the conductivity in Drude theory (the more conductive, the more reflective). By fitting the curve of reflectivity, the conductivity you deduce is call optical, because it comes from optical excitation (optical frequency) contrarily to the conductivity you would deduce from Hall effect measurement (frequency = 0 : continuous).

The Drude theory applies to metal and semiconductor doped to degeneracy (it works for ex for Ag and for ITO).

Since the optical conductivity is a tool to measure the electronic structure, is it related to "moss burstein effect"?

in a sense yes, if you analyse the evolution of the gap by optical measurement, and relate it to the carrier density (either measured by Hall effect for ex, or deduced from fits of your spectra). you can reconstruct the Bustein moss dependency of the gap with n like that.

The plasmonic effect that you mention can come from free carriers in a semiconductor as well.

In fact we have investigated in briefly iodized nanostructured silver films a so-called plasmon-exciton transition. Plasmons here can come from either Ag or Ag-AgI nanocomposite while excitons come from the I-VII semiconductor. Ultimately one talks about the dielectric function/dielectric response of a material epsilon which is a function of angular frequency omega and the wave vector q which is related to the wavelength of the exciting radiation. Dielectric function connects to the electronic band structure! A very very interesting game this!!

can anyone tell me how to calculate optical band gap and optical conductivity theoretically by means of DFT?

Using Wien2k-code, one can find the band gap and optical conductivity with appropriate exchange correlation function for the material under consideration.