Theory of vibrationally inelastic electron transport through molecular bridges

Abstract

Vibrationally inelastic electron transport through a molecular bridge that is connected to two leads is investigated. The study is based on a generic model of vibrational excitation in resonant transmission of electrons through a molecular junction. Employing methods from electron-molecule scattering theory, the transmittance through the molecular bridge can be evaluated numerically exactly. The current through the junction is obtained approximately using a Landauer-type formula. Considering different parameter regimes, which include both the case of a molecular bridge that is weakly coupled to the leads, resulting in narrow resonance structures, and the opposite case of a broad resonance caused by strong interaction with the leads, we investigate the characteristic effects of coherent and dissipative vibrational motion on the electron transport. Furthermore, the validity of widely used approximations such as the wideband approximation and the restriction to elastic transport mechanisms is investigated in some detail.

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

“…(19), the coefficients in front of ρ (0,1) |s 1 agree in Eqs. (33) and (34), which confirms the assumption in Eq. (32).…”

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

“…(19), the coefficients in front of ρ (0,1) |s 1 agree in Eqs. (33) and (34), which confirms the assumption in Eq. (32).…”

Charge transport through a flexible molecular junction

“…We have also investigated the validity of approximate methods, in particular the purely elastic description of the transmission process and the adiabatic nuclei approximation. As was found in our previous study for models with small amplitude motion [23], the purely elastic calculation typically predicts much too narrow transmission probabilities. The adiabatic nuclear approximation, on the other hand, which takes into account the 'static' effect of the vibrational degrees of freedom due to their initial distribution, can describe the average transmission probability rather well, but it is not capable of describing the vibrational excitation accompanying the electron transport.…”

Non-coherent transport in carbon chains

“…before phonon scattering, and is used in the conductance figures presented in this work. The conductance modulations owing to inelastic scattering that we report here bear some resemblance to the inelastic scattering in model calculations in which e-ph coupling effects are presented versus zero-bias carrier injection energy [51][52][53]. There are some differences as well, however, as while in these works both reduction and increase of conduction are observed depending on the carrier energy, e-ph coupling in the present work only causes conductance reduction.…”

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

“…(19), the coefficients in front of ρ (0,1) |s 1 agree in Eqs. (33) and (34), which confirms the assumption in Eq. (32).…”

Charge transport through a flexible molecular junction

“…We have also investigated the validity of approximate methods, in particular the purely elastic description of the transmission process and the adiabatic nuclei approximation. As was found in our previous study for models with small amplitude motion [23], the purely elastic calculation typically predicts much too narrow transmission probabilities. The adiabatic nuclear approximation, on the other hand, which takes into account the 'static' effect of the vibrational degrees of freedom due to their initial distribution, can describe the average transmission probability rather well, but it is not capable of describing the vibrational excitation accompanying the electron transport.…”

Non-coherent transport in carbon chains

“…before phonon scattering, and is used in the conductance figures presented in this work. The conductance modulations owing to inelastic scattering that we report here bear some resemblance to the inelastic scattering in model calculations in which e-ph coupling effects are presented versus zero-bias carrier injection energy [51][52][53]. There are some differences as well, however, as while in these works both reduction and increase of conduction are observed depending on the carrier energy, e-ph coupling in the present work only causes conductance reduction.…”

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

“…(19), the coefficients in front of ρ (0,1) |s 1 agree in Eqs. (33) and (34), which confirms the assumption in Eq. (32).…”

Charge transport through a flexible molecular junction

“…We have also investigated the validity of approximate methods, in particular the purely elastic description of the transmission process and the adiabatic nuclei approximation. As was found in our previous study for models with small amplitude motion [23], the purely elastic calculation typically predicts much too narrow transmission probabilities. The adiabatic nuclear approximation, on the other hand, which takes into account the 'static' effect of the vibrational degrees of freedom due to their initial distribution, can describe the average transmission probability rather well, but it is not capable of describing the vibrational excitation accompanying the electron transport.…”

Non-coherent transport in carbon chains

“…before phonon scattering, and is used in the conductance figures presented in this work. The conductance modulations owing to inelastic scattering that we report here bear some resemblance to the inelastic scattering in model calculations in which e-ph coupling effects are presented versus zero-bias carrier injection energy [51][52][53]. There are some differences as well, however, as while in these works both reduction and increase of conduction are observed depending on the carrier energy, e-ph coupling in the present work only causes conductance reduction.…”