We begin by graphically understanding the transport coe cients in a two-band model (Figure ). Assuming bands that are isotropic and parabolic, squared velocity varies linearly with energy E as v where v(E), g(E), and ⌧ (E) are the energy-dependent velocity, density of states, and scattering time (assuming deformation potential scattering, r = 1/2), respectively. ⌃(E) is sampled by the selection function @f /@E, shown in (e), and weighted by (E E F ) m to obtain (f) the electrical conductivity (m = 0), (g) Seebeck coe cient S (m = 1), and (h) the Lorenz number (m = 2), which is related to the electronic thermal conductivity. The area under the curves are proportional to the magnitude of each transport coe cient at a fixed Fermi energy E F .