First Principles explanation of the positive Seebeck coefficient of lithium

Lithium is one of the simplest metals, with negative charge carriers and a nearly free electron dispersion. Experimentally, however, Li is one of a handful of elements (Cu, Ag, Au) where the sign of the Seebeck coefficient ($S$) is not that of the carrier. We calculate $S$ fully from first-principles, within P.B. Allen's formulation of Boltzmann theory. The constant relaxation time approximation fails and gives a sign for $S$ necessarily identical to the carriers. Our calculated $S$ are in excellent agreement with experimental data. In comparison with Na, we demonstrate that, within the simplest non-trivial model for the energy dependency of the electron lifetimes, the rapidly increasing density of states (DOS) is related to the sign of $S$. The exceptional energy dependence of the DOS is beyond the free-electron model, and distorted by the Brillouin Zone edge, a stronger effect in Li than other Alikis. The electron lifetime dependency on energy is central, but details of the electron-phonon interaction are less important, contrary to what has been believed for several decades. The mechanism exposed here may open the door to new ``ambipolar'' thermoelectric materials, with a tunable sign for the thermopower even if either n- or p-type doping is impossible.