Physics of Semiconductors & Nanostructures Lecture 12: Band gaps, widths, masses (Cornell 2017)

[rammerstheman]

Thank you for uploading these lectures, they're really fantastic.

I have a question - when we perform <m|n> we say unless m=n this term is zero. My understanding is this is because we are treating each separate orbital as orthogonal, which I thought means no overlap in wave function. However when we calculate the hopping energy, we perform <m|H|n> which maybe I misunderstand as meaning energy change when electron in orbital m tunnels into orbital n - surely this is only possible if there is some overlap, in which case <m|n> must have a non-zero value for m != n. If this is the case there seems to be a contradiction in the model's assumptions, either the is an overlap or there isn't!

Thank you so much.

This has been massively helping me understand how strain shifts the band gap in 2D semiconductors for my PhD.