 The linear response of a metal to an electric, magnetic or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy.In reciprocal space, the Fermi surface of an ideal Fermi gas is a sphere of radius

formula_18,

determined by the valence electron concentration where formula_19 is the reduced Planck's constant.A material whose Fermi level falls in a gap between bands is an insulator or semiconductor depending on the size of the bandgap.