Thermoelectric three-terminal hopping transport through one-dimensional nanosystems

A two-site nanostructure (e.g., a molecule) bridging two conducting leads and connected to a phonon bath is considered. The two relevant levels closest to the Fermi energy are each connected to its lead. The leads have slightly different temperatures and chemical potentials, and the nanostructure is also coupled to a thermal (third) phonon bath. The $3\times 3$ linear transport (Onsager) matrix is evaluated, along with the ensuing figure of merit, and found to be very favorable for thermoelectric energy conversion.

Figure 1

(a) A two-localized-state ($i$ and $j$, gray points) system coupled to two leads, with temperatures $T_L$ and $T_R$ and chemical potentials ${\mu }_L$ and ${\mu }_R$ (with the choice ${\mu }_L>{\mu }_R$ and $T_L>T_R$). The phonon bath temperature is $T_{ph}$. The localized states are coupled (dashed lines) to the continuum of states in the leads and are also coupled (the wavy line) to the phonon bath. (b) The effective resistors representing the system: The straight blue arrows indicate the net electronic currents, and the wavy brown one represents the phonon heat current, with $G_{1L}$, $G_{2R}$, and $G_{12}$ being the conductances of the tunneling and the hopping resistors, respectively.

Figure 2

(a) The conductance $\ln (G/G_0)$ and thermopower $eS/k_{\mathrm{B}}$; the abscissa gives the number of computations $N_{\mathrm{com}}$. The parameters are $W=800,L_M=20,\xi =3.3$, in units of average nearest-neighbor distance, $T_0=3000$, $T=20$, and the energy-band width is 1090 ($T_0$ and $L_M$ are the Mott[19] temperature and length, defined in the text). (b) The relative change in $S$ as a function of the system length $W/\left(4L_{\mathrm{M}}\right)$, obtained by averaging over ${10}^6$ random configurations. Parameters (except $W$) are the same as in (a).