Strongly Enhanced Thermal Transport in a Lightly Doped Mott Insulator at Low Temperature

We show how a lightly doped Mott insulator has hugely enhanced electronic thermal transport at low temperature. It displays universal behavior independent of the interaction strength when the carriers can be treated as nondegenerate fermions and a nonuniversal “crossover” region where the Lorenz number grows to large values, while still maintaining a large thermoelectric figure of merit. The electron dynamics are described by the Falicov-Kimball model which is solved for arbitrary large on-site correlation with a dynamical mean-field theory algorithm on a Bethe lattice. We show how these results are generic for lightly doped Mott insulators as long as the renormalized Fermi liquid scale is pushed to very low temperature and the system is not magnetically ordered.

Figure 1

The density of states plotted as a function of energy for $U=2.2$ (full line), $U=4$ (dashed line), and $U=5$ (dashed-dotted line). The lower and the upper gap edges are at ${\omega }_{-}(U)$ and ${\omega }_{+}(U)$, respectively.

Figure 2

Chemical potential plotted as a function of temperature for three concentrations of electrons and several values of $U$. The full, dashed, and dashed-dotted curves correspond to the concentrations of $n_c={10}^{-6},{10}^{-5},$ and ${10}^{-4}$ electrons above half filling. For a given $U$, the numerical difference between these three curves is very small at $T=0$. The value of $\mu (0)$ increases rapidly with $U$, as shown by the curves obtained for $U=2.2$ (black), 2.5 (red), 3 (purple), 4 (green), and 5 (blue), respectively. The values of $U$ increase from the bottom to the top for the cluster of curves. The characteristic temperature $T$, obtained for $U=4$, is indicated by the full, dashed and dashed-dotted arrows. The inset shows the low-temperature behavior obtained for $U=4$.

Figure 3

Lorenz number in units of $[k_B/e{]}^2$, thermopower in units of [$k_B/e$], and thermoelectric figure of merit $ZT$ plotted as a function of temperature for the same parameters as in Fig. 2.