Origin of large thermopower in ${\text{LiRh}}_2{\text{O}}_4$: Calculation of the Seebeck coefficient by the combination of local density approximation and dynamical mean-field theory

Motivated by the newly synthesized mixed-valent spinel ${\text{LiRh}}_2{\text{O}}_4$ for which a large thermopower is observed in the metallic cubic phase above 230 K [Y. Okamoto et al., Phys. Rev. Lett. 101, 086404 (2008)], we calculate the Seebeck coefficient by the combination of local density approximation and dynamical mean-field theory $\left(\text{LDA}+\text{DMFT}\right)$. The experimental values are well reproduced not only by $\text{LDA}+\text{DMFT}$ but also by the less involved Boltzmann equation approach. A careful analysis of the latter shows unexpectedly that the origin of the large thermopower shares a common root with a very different oxide: ${\text{Na}}_x{\text{CoO}}_2$. We also discuss how it is possible to further increase the power factor of ${\text{LiRh}}_2{\text{O}}_4$ through doping, which makes the material even more promising for technological applications.

Figure 1

(Color online) Left panel: Band dispersion of the effective three-orbital Hamiltonian (solid line) and total LMTO band structure (dashed line) of ${\text{LiRh}}_2{\text{O}}_4$. Right panel: partial $a_{1g}$ and $e_g^{\pi }$ density of states for the model.

Figure 2

(Color online) $\text{LDA}+\text{DMFT}$(QMC) self-energy calculated by the Pade approximation (left) and a polynomial fit (right).

Figure 3

(Color online) Thermopower calculated by the Boltzmann equation approach and the constant-$\tau$ method, as well as by $\text{LDA}+\text{DMFT}$, using both the Pade approximation and a polynomial fit for the self-energy.

Figure 4

(Color online) Group velocity squared $\left(u_k^2\right)$ along different directions of the first Brillouin zone for ${\text{Rh}}^{+3.5}$ (${\text{LiRh}}_2{\text{O}}_4$; upper panel) and ${\text{Rh}}^{+3.08}$ (electron-doped ${\text{LiRh}}_2{\text{O}}_4$; lower panel). $k$ points above the Fermi energy $E_F$ are shown in yellow (light gray), those below $E_F$ in red (dark gray).

Figure 5

(Color online) Power factor (normalized by its value at Rh $\text{valence}=+3.5$) and thermopower (inset) as a function of the valence of Rh, calculated by the Boltzmann equation.