Thermoelectric properties of elemental metals from first-principles electron-phonon coupling

Abstract

The Seebeck coefficient is one of the key ingredients in thermoelectric properties, and it is often calculated based simply on the electronic band structure, within the frame of Boltzmann's transport theory and the constant relaxation time approximation. Despite the simplicity and popularity of this approximation, its validity is not fully justified even in lightly doped semiconductors, and it breaks down completely in metals. On the other hand, more sophisticated first-principles approaches are available but require the computation of the full electronphonon coupling. Here, we demonstrate with several simple (alkali and noble) metals viz., Li, Na, K, Cu, Ag, Au, and Pt, that the variational approach based on ab initio couplings can reproduce experimental Seebeck coefficients quantitatively, whereas the constant relaxation time approximation yields significant quantitative discrepancies and often fails to predict the correct sign. Calculations of the electrical resistivity of these metals via the variational approach are also reported.

Skewed Non-Fermi Liquids and the Seebeck Effect

“…However, it has been recognized that another source of asymmetry may also influence the Seebeck coefficient: that of the lifetime (scattering rate) of these excitations. Although this has been discussed theoretically [4][5][6][7][8][9][10][11] and put forward as a possible mechanism for materials in which the sign of S is found to be opposite to that predicted by bandstructure [4,12,13], it has received comparatively less attention. One of the reasons is that, as detailed below, the particle-hole asymmetry of the inelastic scattering rate does not influence S at low-temperature for metals obeying Fermi liquid theory when impurity scattering is also present.…”

Efficient hot carrier dynamics in near-infrared photocatalytic metals

“…Accurate theoretical descriptions of catalytic metals, including their electronic [38][39][40][41], vibrational [42][43][44][45], and optical [36,37,46] properties abound. Nonetheless, ab initio calculations addressing the scattering relaxation rates and mean free paths are still scarce.…”

Positive Seebeck coefficient in highly doped La$_{2-x}$Sr$_x$CuO$_4$ ($x$=0.33); its origin and implication

“…This 'reversed sign thermopower' puzzle in Cu, Ag, Au and Li (the alkali metal also showing an unexpected positive Seebeck response) has been addressed by Robinson [19] and more recently by Xu, Di Gennaro and Verstraete [20,21]. Robinson argued that a mean-free-path rapidly decreasing with increasing energy would provide a solution to the puzzle and this can arise due to the structure of the electron-ion pseudopotential.…”

“…Such an energy dependence can arise for different reasons. According to first principle calculations on Li [20,21], a feature in density of states just below the chemical potential skews the available phase space for scattering [20]. In copper, on the other hand, the density of states is flat near the chemical potential [21], and it is the electron-phonon coupling that is energy dependent.…”

“…According to first principle calculations on Li [20,21], a feature in density of states just below the chemical potential skews the available phase space for scattering [20]. In copper, on the other hand, the density of states is flat near the chemical potential [21], and it is the electron-phonon coupling that is energy dependent. Robinson's phenomenological model -invoking a screened electron-ion pseudopotential -leads to a similar conclusion [19].…”