Hi 1) I have read in an article that the atoms in a lattice are at "half-filling". As I understand, this means that the chemical potential is zero. Why does "half-filling" mean since it equals that the chemical potential is zero? 2) Lets say that I place an impurity with potential U0 in my lattice. Does it make a difference whether U0 is positive or negative? What is the usual case? Best regards and happy Easter, Niles.