Increasing thermoelectric performance using coherent transport

We show that coherent electron transport through zero-dimensional systems can be used to tailor the shape of the system’s transmission function. This quantum-engineering approach can be used to enhance the performance of quantum dots or molecules in thermal-to-electric power conversion. Specifically, we show that electron interference in a two-level system can substantially improve the maximum thermoelectric power and the efficiency at maximum power by suppressing parasitic charge flow near the Fermi energy and by reducing electronic heat conduction. We discuss possible realizations of this approach in molecular junctions or quantum dots.

Figure 1

(a) Level positions in the proposed two-level system. (b, c) Possible implementation using zinc porphine, sketching the wave functions of the two almost-degenerate levels close to the Fermi energy; see also Ref.14. The light(dark)-shaded regions indicate a positive(negative) amplitude of the wave function $\Psi$, respectively. By replacing the hydrogen atoms at positions L and R with, for example, sulfur, the molecule can be in contact with leads so that the parities of the wave functions with respect to the leads differ for the two levels.

Figure 2

The power factor for coherent transport through a quantum system with two levels and for $T=300$ K, $\Gamma =3k_{B}T$, and $a=0.6$. Level positions are defined relative to $E_F$. The cross marks the maximum ($S^2\sigma =316$ fW at $E_1=5.80k_{B}T$, $E_2=1.47k_{B}T$), and the transmission function is calculated at this level configuration in Fig. 3a.

Figure 3

(a) Transmission function at the level configuration corresponding to maximum power; see Fig. 2. (b) Maximum power production and (c) efficiency at maximum power ${\eta }_{\max P}$ in units of the Carnot efficiency ${\eta }_C$, as a function of $\Gamma$. (d) ${\eta }_{\max P}^{\Gamma }$ (defined as $P_{\max }$ at the optimal choice of $\Gamma$; see text), with the dashed line marking the one-level result. In (b–d) the temperatures of the two leads are given by $T_L=330$ K and $T_R=300$ K.

Figure 4

(a) Thermoelectric figure of merit $Z{T}_{\mathrm{el}}$ for coherent transport as a function of level configuration for $T=300$ K. The parameters $\Gamma =3k_{B}T$ and $a=0.6$ match the conditions for maximum power in Fig. 3b. (b) The thermopower $S$ calculated for $U=0$ and $U=10k_B{T}_{\mathrm{mean}}$, $\Gamma =k_B{T}_{\mathrm{mean}}$, $a=0.7$, and $\Delta T=0.1k_B{T}_{\mathrm{mean}}$. The second level is positioned at $E_2=k_B{T}_{\mathrm{mean}}$.