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Can we have band gap anywhere?

by hokhani
Tags: band
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hokhani
#1
Jul14-14, 10:56 AM
P: 269
According to solid state texts in Brillouin zone borders where diffraction condition satisfies we have a band gap. However I usually see Band gaps which are located in the center of Brillouin zone. Please correct me if I am wrong.
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rigetFrog
#2
Jul14-14, 04:35 PM
P: 109
which text are you reading?
hokhani
#3
Jul14-14, 05:51 PM
P: 269
Quote Quote by rigetFrog View Post
which text are you reading?
In "solid state physics, Ashcroft - Mermin, chapter 9, electrons in a weak periodic potential", it is explained that due to weak perturbation we have energy gap at Brillouin zone border. Moreover we now for example that in GaAs the energy gap is at K=0 (Gamma point) which is not at the Brillouin zone border.

rigetFrog
#4
Jul14-14, 06:28 PM
P: 109
Can we have band gap anywhere?

I'm sure where to start.

Do you understand how a weak periodic potential gives rise to a bandgap?

Liboff's quantum textbook has a nice derivation using perturbation theory.

Alternatively, you could use Fermi's golden rule using the weak periodic potential at the perturbing hamiltonian.


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