Interplay between electron–electron and electron–vibration interactions on the thermoelectric properties of molecular junctions

Abstract

The linear and non-linear thermoelectric properties of molecular junctions are theoretically studied close to room temperature within a model including electron-electron and electron-vibration interactions on the molecule. A non-equilibrium adiabatic approach is devised to include a strong Coulomb repulsion and applied to the self-consistent calculation of electron and phonon transport properties of massive molecules, such as fullerenes, within the Coulomb blockade regime. We show that the phonon thermal conductance is quite sensitive to strong electron-electron interactions within the intermediate electron-vibration coupling regime. Furthermore, the electron-vibration interaction enhances both phonon and electron thermal conductance, and it reduces not only the charge conductance, but also the thermopower. The effect of the strong electron-electron interactions provides a peculiar double-peak structure to the thermopower versus charge conductance curve. Finally, within the regime of weak to intermediate electron-vibration and vibration-lead phonon coupling, the peak values of the thermoelectric figure of merit are slightly less than unity, and the maximal efficiency of the junction can reach values slightly less than half of the Carnot limit for large temperature differences between the leads. Recently, the possibility of controlling materials at the nanoscale has been exploited to optimize the thermoelectric efficiency [4,6,7]. For example, a maximum ZT 2.4 ≃ has been observed at room temperature in Bi Te Sb Te 2 3 2 3 superlattice thermoelectric devices [8]. High values of ZT have been reported in quantum dot superlattices [9] and in semiconductor nanowires [10], where phonon confinement can lead to a lower phonon thermal conductance [11,12]. Actually, a significant reduction in lattice thermal conductivity is considered as the main route for having high ZT in low-dimensional materials [13]. The improvement of thermoelectric efficiency can also derive from the discreteness of energy levels in nanostructures resulting into a violation of the OPEN ACCESS

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

“…For the sake of simplicity, we do not include explicitly the effect of the Coulomb repulsion on the quantum dot Hamiltonian in deriving equations encoding the adiabatic approximation. In section 5, we will show that, in the particular case of a single-level quantum dot with large repulsion U , the adiabatic approach works exactly as in the non-interacting case with the “caveat” of treating each Green’s function pole as a non-interacting level [ 82 ].…”

“…In the previous sections, we have seen that, one of the main effects of an adiabatic oscillator on the spectral peak at finite temperature is to give an extra broadening and a shift proportional to the oscillator–oscillator coupling energy E P . We therefore expect that, in the presence of an adiabatic oscillator ≤ k B T one can perturb each spectral peak of the quantum dot independently, obtaining (see details in [ 82 ]) at the zero-th order of the adiabatic approach…”

“…with the lesser Green’s function G < (ω, x ) = ( i /2)[ f L (ω) + f R (ω)] A (ω, x ). The above approximation is valid if the electron–oscillator interaction is not too large, such that and the peaks of the spectral function can be still resolved [ 82 ].…”

“…Before discussing the numerical results, it is useful to analyze the properties of the electron–oscillator damping rate θ′( x ) = θ( x )/ m , with θ( x ) defined in Eq. 18 (explicitly calculated in [ 82 ]) and appearing explicitly in the Langevin equation of the oscillator. The amplitude of the peaks of θ′( x ), although increasing as a function of the electron–oscillator coupling E P , is always smaller than the damping contribution (the realistic value γ = 0.15 is assumed in the second part of this section) coming from the coupling with the phononic leads.…”

Electrothermal Transistor Effect and Cyclic Electronic Currents in Multithermal Charge Transfer Networks

“…Similarly, thermoelectric phenomena in such junctions [2], where molecules connect between electrodes of different temperatures, are usually treated (with a few exceptions, e.g., Refs. [3][4][5][6][7][8][9][10][11][12]) with electron-vibration interaction disregarded. This stands in contrast to electron transfer reactions in condensed molecular systems that are usually dominated by hopping between thermally equilibrated polaron-like states as described by Marcus theory [13][14][15][16] (analogous kinetics in junction transport is known, mostly in so called redox molecular junctions [17,18]).…”