S. Scandolo, ICTP

Lesson 16 (Crystals: electric transport)

The discussion of optical properties of crystals continues. For insulators, there is an energy gap between the excited states and the ground state. This means that insulators can be transparent if the energy gap is larger than the energy of visible light (roughly 3eV). However, this is not so different in the case of metals in this model. Photons cannot excite within the band due to the conservation of momentum (see the previous lecture). In reality, metals are not transparent. The explanation derives from impurities which make low energy transitions possible.

The electric transport property of metals can also be discussed in the framework of electron bands.The professor proves that the momentum of an energy eigenstate is given by the . From classical mechanics, it is known that a static enectric field would transfer energy in time. This means , from which.