- Suppose we let the hoppings of the monatomic chain alternate between two slightly different values (see the sketch in the figure of exercise 2), thereby increasing the size of the unit cell. At what value of k do you expect band gaps to open in the dispersion derived in warmup question 3?
I don’t fully understand what a band gap is, why it opens up at a certain k and at what energy this would happen. Can someone help?
If you look at the first plot in this unit’s lecture notes, you will find two branches. If you scan it in frequency, you will see that some frequencies don’t have an assigned dispersion relation. That is what we call a band gap. You can also see it in the density of states where there are two “bands” of energy with available states, and in between, there is a “gap”.
At a certain value of k in the dispersion relation, you find a place where the distance between the two branches is the smallest, which is the value of k they are asking for. Hope that helps! Let me know.
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