First Principles Explanation of the Positive Seebeck Coefficient of Lithium

Abstract

Lithium is one of the simplest metals, with negative charge carriers and a close reproduction of free electron dispersion. Experimentally, however, Li is one of a handful of elemental solids (along with Cu, Ag, Au etc.) where the sign of the Seebeck coefficient (S) is opposite to that of the carrier. This counterintuitive behavior still lacks a satisfactory interpretation. We calculate S fully from firstprinciples, within the framework of P.B. Allen's formulation of Boltzmann transport theory. Here it is crucial to avoid the constant relaxation time approximation, which gives a sign for S which is necessarily that of the carriers. Our calculated S are in excellent agreement with experimental data, up to the melting point. In comparison with another alkali metal 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) across the Fermi energy is related to the sign of S in Li. The exceptional energy dependence of the DOS is beyond the free-electron model, as the dispersion is distorted by the Brillouin Zone edge, a stronger effect in Li than other Aliki metals. The electron lifetime dependency on energy is central, but the details of the electron-phonon interaction are found to be less important, contrary to what has been believed for several decades. Band engineering combined with 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.PACS numbers: 72.15. Jf,72.15.Lh,72.15.Eb,72.10.Di,71.20.Dg Thermoelectricity (TE) has drawn much attention over the past century [1,2] as an effective way of producing electricity from heat energy, or vice versa. In addition to applications in waste heat recovery, the reversible functionality of TE materials also enables heating and refrigeration within the same unit. Spot cooling[3] of computer processors can be achieved with TE devices of small size and without moving parts. The efficiency of current thermoelectric devices is relatively low compared to, e.g., thermal engines, which limits their applications.[1] In the search for a good thermoelectric material, a large Seebeck coefficient (S) is one of the central components in the figure of merit, where it appears squared. Most advances in TE have however targeted the simpler tasks of lowering the thermal conductivity, [4] or optimizing the electron density of states [5]. The magnitude of S is also important in other applications, e.g. for thermal sensors.[6] Though S can be measured straightforwardly in experiment and calculated theoretically within certain approximations, a complete microscopic understanding, and paths for systematic improvement of S are still lacking. The most common approach is to consider a constant averaged relaxation time for the electrons (τ ). The relaxation time approximation (RTA) works in a surprisingly large number of cases, but has little formal justification, and we expos...

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