So, the Fermi level in crystals is pretty easy to understand. Been using it and talking about it in terms of the highest occupied level forever. However, I'm now reading about disordered systems. A lot of researchers mention the existence of empty states randomly distributed above and below the Fermi level. But isn't the Fermi level necessarily the energy at which all energies below are filled states?
EDIT: So I suppose chemical potential is the more correct term to use (instead of Fermi energy) because not at T = 0. Anyways, consider this quote: "the localized gap states near $E_F$ are spread in energy with singly occupied gap states below $E_F$, doubly occupied states lying above $E_F$, and empty states distributed randomly."