Could intraband transition (in metals) of an electron in the conduction band produce a hole there?
The hole concept is related to a missing electron in the valence band. The valence band of a metal is completely filled and the electrons in the conduction band are FREE to begin with.
Therefore, there is no such thing as a hole in metals.
Ok, but as far as I know, the hole at the point k is a concept which is contributed to the electron at the point -k. Until the electron at k is not removed, its effect is neutralized by the electron at -k but if it is removed, the electron at -k participates in conduction which its conduction is attributed to the hole at k. This situation could happen in the conduction band as if we have one electron at k and another at -k and if the electron at k moves to any different state, why we wouldn't have the hole at k?
because an electron state in a metal conduction band has a de-localized wave function. It can contribute to conduction without having to transition to another band as in a semiconductor. Of course, it is more intersting to ask what happens when an electron is removed as in photoelectric effect.. do you see a creation of a hole? No.. because the valance band is completely filled and
Yes, but the hole, like the excited electron, will quickly relax and be scattered to the vicinity of the Fermi surface. They behave differently than holes in the valence band in so far as their effective mass is negative. As their charge is also positive (that of the electron being negative), they will move in an applied field in the same direction as the electrons, so there won't be a charge separation as in a semi-conductor.
These kind of holes are also important in the formation of superconductors.
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