What is the meaning of the zero point of the real part of the dielectric function for a semiconductor? I basically understand the zero point of the real part of the dielectric function for a metal. It generally corresponds to plasmon. For a metal, if the frequency is lower, the real part is negative meaning that the light is completely reflected. The electrons around the surface can screen the electric fields of the light before it gets into the bulk. But if the frequency is higher than the plasmon frequency, the real part is positive and the metal behaves like a dielectric medium.

But I cannot get a physical understanding of the similar zero points for a semiconductor like silicon. Could anyone please help me on this?

• The figure is from Phys. Rev. B 62,7071 and they are the plots of the real and imaginary part of the dielectric function of silicon. – John Cao Feb 23 '16 at 13:38

I would say that it corresponds to some kind of quasiparticle or in other words an elementary excitation of the system. The kind of excitation that can be responsible for the particular zero of $Re\left[\epsilon\right]$ you are looking it depends on what frequency it is at.
In the example you gave we have the zero approximately at $\omega \approx 4eV$. This corresponds to (now working with the light dispersion since that is what is getting absorbed): $\lambda \approx 3 \cdot 10^{-7}m$ which is in the ultraviolet. This is most likely still a plasmon of some kind, i.e. an oscillation of the electron gas (see also comment about semiconductor plasmons here).
• Basically you are correct and I think it is important to find and understand the quasiparticle or transitions. According to Fig.11 in PHYSICAL REVIEW B 69, 245419 (2004), the zero point in my question seems to be related to the interband transition $\sigma\rightarrow\sigma^*$ – John Cao Feb 25 '16 at 11:39