Potassium has Fermi energy and a periodic-potential amplitude
PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure
Condensed Matter Physics, Ch Electrons in a periodic potential: Bloch's theorem and the opening of a gap
Problem
Potassium has Fermi energy EF=2.12eV and a periodic-potential amplitude ∣UG∣≈0.25eV. Rock salt (sodium chloride) has a filled band about 3.0eV wide, separated from the next, empty band by a gap of about 8.5eV.
((a)) Using the chapter's criterion, compute the ratio that decides whether the weak-potential picture is trustworthy for potassium.
((b)) Compute the corresponding ratio (gap to bandwidth) for rock salt.
((c)) Say, for each solid, whether the weak-potential picture of this chapter deserves trust, and why.