Thermoelectric transport in strongly correlated quantum dot nanocomposites

We investigate the thermoelectric transport properties (electrical conductivity, Seebeck coefficient, power factor, and thermoelectric figure of merit) in strongly correlated quantum dot nanocomposites at low temperature (77 K) by using the dynamical mean-field theory and the Kubo formula. The periodic Anderson model is applied to describe the strongly correlated quantum dot nanocomposites with tunable parameters such as the size of quantum dots and the electron occupation number. The electron occupation number can be controlled by the doping concentration in the both matrix and quantum dots, the size of quantum dots, and the interdot spacing. These parameters control the transition between $n$-type like behavior (with negative Seebeck coefficient) and $p$-type like behavior (with positive Seebeck coefficient) of strongly correlated quantum dot nanocomposites. Large Seebeck coefficient up to $260\mu \text{V}/\text{K}$ due to the asymmetry of the electron bands with sharp electron density of states can be obtained in the strongly correlated quantum dot nanocomposites, along with moderate electrical conductivity values in the order of ${10}^5/\Omega \text{m}$. This results in optimal power factor about $78\mu \text{W}/\text{cm}{\text{K}}^2$ and optimal figure of merit $\left(ZT\right)$ over 0.55 which is much larger than the value of the state-of-the-art low-temperature thermoelectric materials. This study shows that high efficiency thermoelectric materials at low temperature can be obtained in strongly correlated quantum dot nanocomposites.

Figure 1

(Color online) (a) Schematic of simple cubic lattice quantum dot nanocomposites with QDs periodically distributed in the matrix. The dots represent spherical QDs with a size $D$. The distance between the nearest-neighboring QDs is $a$. (b) Schematic band diagram of the quantum dot nanocomposites with the lowest two energy levels in QDs. ${\epsilon }_d$ is the energy level of the localized electron in QD, $U$ is the Coulomb interaction, ${\epsilon }_c$ is the conduction band minima in matrix, $E_{dot}$ is the energy difference between the conduction band minima of QD material and ${\epsilon }_c$, and $D$ is the diameter of the QD.

Figure 2

(Color online) DOS of conduction electrons for different hybridization constant $t$ when $n_{tot}=2$ and (a) $D=4\text{nm}$, (b) $D=3.6\text{nm}$. (c) DOS of conduction electrons for different $D$ when $n_{tot}=2$ and $t=0.05\text{eV}$. (d) DOS of conduction electrons for different $n_{tot}$ when $D=4\text{nm}$ and $t=0.05\text{eV}$. All cases used $T=77\text{K}$ and $a=10\text{nm}$ for calculations.

Figure 3

(Color online) The dependence of chemical potential on (a) the size of QDs $D$ for different electron occupation number $n_{tot}=1.8$, 2, and 2.2, and (b) $n_{tot}$ for different size of QDs $D=3.6$, 3.8, and 4 nm. The calculation uses $t=0.05\text{eV}$, $T=77\text{K}$, and $a=10\text{nm}$.

Figure 4

(Color online) (a) DOS in QD as a function of the size of QDs $D$ when $n_{tot}=2$, (b) TDF as a function of the size of QDs $D$ when $n_{tot}=2$, (c) DOS in QD for different $n_{tot}$ when $D=4\text{nm}$, (d) TDF for different $n_{tot}$ when $D=4\text{nm}$. All the calculations used $a=10\text{nm}$, $t=0.05\text{eV}$, and $T=77\text{K}$.

Figure 5

(Color online) The dependence of (a) electrical conductivity and Seebeck coefficient, and (b) power factor on the size of the QDs $D$ for different electron occupation number $n_{tot}=1.8$, 2, and 2.2. The calculation uses inputs as $a=10\text{nm}$, $\delta =3.6\text{meV}$, $t=0.05\text{eV}$, and $T=77\text{K}$.

Figure 6

(Color online) The dependence of (a) electrical conductivity and Seebeck coefficient, and (b) power factor on $n_{tot}$ for different size of QDs $D=3.6$, 3.8, and 4 nm. The calculation uses inputs as $a=10\text{nm}$, $\delta =3.6\text{meV}$, $t=0.05\text{eV}$, and $T=77\text{K}$.

Figure 7

(Color online) The dependence of $ZT$ on (a) $D$ for different $n_{tot}=1.8$, 1.9, and 2 (b) on $n_{tot}$ for different $D=3.6$, 3.8, and 4 nm. The calculation uses inputs as $a=10\text{nm}$, $\delta =3.6\text{meV}$, $t=0.05\text{eV}$, $T=77\text{K}$, and ${\kappa }_l=0.5\text{W}/\text{mK}$.

Figure 8

(Color online) (a) Electron concentration $\rho$ and occupation number $n$ versus $D$ when $n_{tot}=2$ and $a=10\text{nm}$. (b) Electron concentration $\rho$ and occupation number $n$ versus $n_{tot}$ when $D=4\text{nm}$ and $a=10\text{nm}$. Solid curve: electron density in matrix. Dashed curve: electron density in QD. Solid curve with dot: occupation number in matrix. Dashed curve with dot: occupation number in QD. $T=77\text{K}$. (c) Electron density as a function of $a$ for fixed $D$ and $n_{tot}$.