Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

Abstract

We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double quantum dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic-a truncated (twostate) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second-order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.

Effects of vibrational anharmonicity on molecular electronic conduction and thermoelectric efficiency

“…Remarkably, we find that in agreement with previous results on the two-state anharmonic mode 26,41 , while the I-V characteristics significantly deviate under different anharmonic potentials, the Seebeck coefficient and the thermoelectric efficiency, even beyond linear response, manifest a weak sensitivity to the vibrational potential.…”

“…Since many levels contribute to the currents at this high temperaturehigh bias limit, we cannot put forward a simple argument justifying this correspondence. We know however, from analytical considerations, that the harmonic oscillator case and the two-state mode build up an identical thermoelectric energy conversion efficiency 26 . Additional work is required to clarify on this correspondence in highly-biased, high-T , genuinely anharmonic models.…”

“…Refs. [24][25][26] . It is important, however, to examine nanojunctions beyond the ideal harmonic-mode limit and understand the role of vibrational anharmonicity on electronic transport through molecules.…”

“…18,26 we derived the cumulant generating function of the phonon-assisted donor-acceptor model with either a harmonic mode or a two-state impurity. We then showed that while the inelastic current and its cumulants exhibited significant signatures of molecular anharmonicity, the thermoelectric energy conversion efficiency was indifferent to the nature of the mode; it was precisely identical when working with either a harmonic local mode, or a two-level system 26,41 . This result was obtained under the weak electron-vibration coupling approximation, but allowing for strong metal-molecule hybridization.…”

Thermopower of molecular junctions: Tunneling to hopping crossover in DNA

“…Focusing on works reporting on both G and S, we note that most computational studies of linear-response transport coefficients in single molecules are limited to the coherent limit 23 , using the Landauer formula with parameters derived from first principle calculations [24][25][26][27][28][29][30][31][32][33][34] , or other coherent-transport approaches 35 . Effects of vibrations on the thermopower were assessed using scattering approaches 36,37 , or perturbatively using non-equilibrium Green's function (NEGF) [38][39][40][41][42][43] or quantum master equation (QME) methods [42][43][44][45][46] . However, given the computational cost, such treatments are limited to describe rather small systems with few (1-2) molecular electronic orbitals and 1-2 primary vibrational modes.…”