Resonant enhancement of thermoelectric properties by correlated hopping for the Falicov-Kimball model on Bethe lattice

The effect of correlated hopping on the charge and heat transport of strongly correlated particles is studied for the Falicov-Kimball model on the Bethe lattice. Exact solutions for the one-particle density of states (DOS) and two-particle transport function (the “quasiparticle” scattering time) are derived using dynamical mean-field theory. For a wide range of the correlated hopping, the transport function exhibits singularities due to the resonant two-particle contribution, whereas the one-particle DOS does not show any anomalous features. By tuning the number of itinerant electrons, so as to bring the Fermi level close to the resonant frequency, we get a large increase of the electrical and thermal conductivities, and the thermoelectric power. When the hopping amplitude between the occupied sites is reduced sufficiently, the itinerant electrons localize in the clusters of sites occupied by $f$ electrons. This gives rise to an additional narrow band in the DOS between the lower and upper Hubbard bands but has only a minor effect on the thermoelectric properties.

Figure 1

The density of states $A_d\left(\omega \right)$, left panels (a), (c), (e), and transport function $I\left(\omega \right)$, right panels (b), (d), (f), shown as a function of frequency $\omega$ and correlated hopping parameter $t_2$ on a false color plot for $U=0.25, t_3=0$, and for $f$-particle concentrations (a,b) $n_f=0.5$, (c,d) 0.75, and (e,f) 0.9 (top to bottom). Inserts represent enlarged rectangular areas with (a,b) $t_2\in [-0.53,-0.47], \omega +{\mu }_d\in [0.2,0.3]$; (c,d) $t_2\in [-0.6,-0.4], \omega +{\mu }_d\in [0.0,0.5]$; and (e,f) $t_2\in [-0.65,-0.35], \omega +{\mu }_d\in [-0.4,0.6]$. Dashed line indicates the resonant frequency ${\omega }_{\text{res}}$ given by Eq. (46).

Figure 2

Same as in Fig. 1 for $U=2$. Inserts represent enlarged rectangular areas with $t_2\in [-0.6,-0.4], \omega +{\mu }_d\in [1.8,2.4]$.

Figure 3

The interacting DOS (panel a) and transport function (panel b) plotted versus frequency for $U=0.25$ at half filling ($n_f=n_d=1/2$) and for $t_2=-0.1, -0.05$, 0, 0.05, 0.1 ($t_3=0$). The Fermi level $E_{\mathrm{F}}$ depends on the hopping $t_2$, and the gray arrow indicates a narrow frequency interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 4

Temperature dependences of the dc conductivity ${\sigma }_{\mathrm{dc}}$, thermal conductivity ${\kappa }_{\mathrm{e}}$, and Seebeck coefficient $S$ for the same parameters as in Fig. 3.

Figure 5

The interacting DOS (panel a) and transport function (panel b) plotted versus frequency for $U=0.25, n_f=0.75$, and $n_d=1-n_f=0.25$, and for $t_2=-0.1, -0.03$, 0, 0.03, 0.1. The gray arrow indicates a narrow $\omega$ interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 6

Temperature dependences of the dc conductivity ${\sigma }_{\mathrm{dc}}$, thermal conductivity ${\kappa }_{\mathrm{e}}$, and Seebeck coefficient $S$ are shown for the same parameters as in Fig. 5.

Figure 7

The interacting DOS (panel a) and transport function (panel b) plotted versus $\omega$ for $U=0.25$ at half filling ($n_f=n_d=1/2$) and for $t_2=-0.47, -0.5, -0.53$ ($t_3=0$). The gray arrow indicates a narrow $\omega$ interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 8

Temperature dependences of the (a) dc conductivity ${\sigma }_{\mathrm{dc}}$, (b) thermal conductivity ${\kappa }_{\mathrm{e}}$, and (c) Seebeck coefficient $S$ are shown for the same parameters as in Fig. 7.

Figure 9

The interacting DOS (panel a) and transport function (panel b) plotted versus $\omega$ for $U=0.25, n_f=0.75, n_d=1-n_f=0.25$, and for $t_2=-0.46, -0.48, -0.5, -0.52, -0.54$. Labels 1, 2, and 3 denote the lower Hubbard band, the upper Hubbard band, and band of localized states, respectively. The gray arrow indicates a narrow $\omega$ interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 10

Temperature dependence of the (a) dc conductivity ${\sigma }_{\mathrm{dc}}$, (b) thermal conductivity ${\kappa }_{\mathrm{e}}$, and (c) Seebeck coefficient $S$ in the weak-coupling regime is shown for the same parameters as in Fig. 9.

Figure 11

The interacting DOS (panel a) and transport function (panel b) is plotted versus $\omega$ for $U=2$ at half filling ($n_f=n_d=1/2$) and for $t_2=-0.45, -0.5, -0.55$ ($t_3=0$). The gray arrow indicates a narrow $\omega$ interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 12

Temperature dependence of the dc conductivity ${\sigma }_{\mathrm{dc}}$, the thermal conductivity ${\kappa }_{\mathrm{e}}$, and Seebeck coefficient $S$ in the strong-coupling regime is shown for the same parameters as in Fig. 11.

Figure 13

The interacting DOS (panel a) and transport function (panel b) for $U=2$ and $n_f=0.75$, and $n_d=1-n_f=0.25$. Here, $t_2=-0.45, -0.496, -0.5, -0.504, -0.55$ and labels 1, 2, and 3 denote the lower Hubbard band, the upper Hubbard band, and the band of localized states, respectively. The gray arrow indicates a narrow $\omega$ interval in which $E_{\mathrm{F}}$ is located for different values of $t_2$.

Figure 14

Temperature dependence of the dc conductivity ${\sigma }_{\mathrm{dc}}$, the thermal conductivity ${\kappa }_{\mathrm{e}}$, and Seebeck coefficient $S$ for the same parameters as in Fig. 13.