From what I know, speed of light is c in vacuum.

 

However, it seems to slow down as it pass through transparent material like glass or water.

 

I have learned that light has actually not slowed down as it pass through glass, it only appears to slow down. Actually, the speed of light is still c as it pass through glass, but the electronic polarization effects of the material causes EM energy to be absorbed through dielectric loss (due to the imaginary dielectric constant) and this in effect make light appear to us as having slowed down in the glass medium.

 

Assuming magnetic effects of the EM radiation to be negligible in glass, we have the relationship refractive index n = square root of dielectric constant assuming square root of magnetic permeability to be one.

 

However, how does this EM energy being absorbed? What is the real mechanism behind this. Is it due to energy bands and bandgap?

The QED explanation is that the photons are being absorbed and re-emitted by virtual states of the medium. The absorption/emission time delay causes the slowdown, but the photons travel at c. If the photon is absorbed and a real state is involved, there will be scattering and loss.

 

The classical explanation is that the permittivity and permeability change, causing the wave propagation speed to be smaller.

Mmm, what do you mean by virtual states? All the energy states should be acounted for in QM, in materials as complicated as dielectrics, metals and semiconductors, there are allowed bands (in which all your allowed energy states lie) and forbidden bands (in which all the electrons cannot possess that energy level). In dielectrics, the forbidden energy gap between the conduction band and the valence band is so much greater, about 5eV or more, but where do this virtual states lie in the energy band diagram?

Mmm, what do you mean by virtual states? All the energy states should be acounted for in QM, in materials as complicated as dielectrics, metals and semiconductors, there are allowed bands (in which all your allowed energy states lie) and forbidden bands (in which all the electrons cannot possess that energy level). In dielectrics, the forbidden energy gap between the conduction band and the valence band is so much greater, about 5eV or more, but where do this virtual states lie in the energy band diagram?

 

Virtual states can have any energy, AFAIK. They are not real states, which is what you are describing.