If the chemical potential happened to be in the middle of a gap you couldn't have charge accumulation on the edges: indeed you would have a band completely filled and because of Pauli principle you couldn't have place for other electrons IN THE SAME band. So you should put them in the upper band, but the electrons do not have enough energy to do so because that would require the overcoming of the energy gap. On the contrary if the chemical potential is not inside a gap the next not occupiable state is not on another band separated by an energy gap. so you may indeed find place for these extra electrons
@@mr-vj6doI’m just implying they need a dependable sampling. I may be missing facts or mistaken. You have to consider some time you have no.s going the same spin direction in time and are different than the other no.s involved
@4:30, why the edge modes should be gapless?
If the chemical potential happened to be in the middle of a gap you couldn't have charge accumulation on the edges: indeed you would have a band completely filled and because of Pauli principle you couldn't have place for other electrons IN THE SAME band. So you should put them in the upper band, but the electrons do not have enough energy to do so because that would require the overcoming of the energy gap. On the contrary if the chemical potential is not inside a gap the next not occupiable state is not on another band separated by an energy gap. so you may indeed find place for these extra electrons
How could they not help being gapless. The gap is so very important
@@mr-vj6doI’m just implying they need a dependable sampling. I may be missing facts or mistaken. You have to consider some time you have no.s going the same spin direction in time and are different than the other no.s involved