Photoinduced anomalous Coulomb blockade and the role of triplet states in electron transport through an irradiated molecular transistor. II. Effects of electron-phonon coupling and vibrational relaxation

Abstract

We generalize our previous theory [Nano Lett. 18, 5015-5023 (2018)] to investigate the influence of electron-phonon (e-p) coupling and vibrational relaxation on photoinduced anomalous Coulomb blockade, which originates from the triplet states and the energy level alignment. We derive the master equation for an irradiated molecular transistor and obtain the relevant rates via the Redfield theory instead of the phenomenological Fermi golden rule approach. To explore the interplay between e-p coupling and vibrational relaxation, we analyze the charge stability diagrams and the current-voltage characteristics (both gate voltage and source-drain bias voltage) under different e-p coupling strengths in two extreme limits of vibrational relaxation (equilibrated and unequilibrated phonon regimes). From the perspective of energy level alignment, we choose four representative situations and derive the analytical formulas of the photoinduced current in the equilibrated regime. The analytical solution reveals a new type of photocurrent due to e-p coupling that does not require the perfect energy level alignment between charged states and triplet states. In general, our study indicates that photoinduced current and anomalous Coulomb blockade caused by the triplet states are supposed to be experimentally observed.

Light Induced Negative Differential Conductance in Molecular Junctions: Role of Triplet States and Electron-Phonon Interaction

“…The electronic state energies are obtained to be E S0 = 0, E S1 = 3.029 eV, E T = 1.871 eV, E C = 6.178 eV and E A = −1.365 eV, in which for the anion and cation states an image charge correction of -0.3 eV is considered [32]. Moreover, the non-biased chemical potential of the metallic leads is assumed to be µ 0 = −5.3 eV.…”

“…By exploiting a polaron transformation and considering Born-Markov approximation in accordance to the weak molecule-lead coupling (a straight forward generalization of the derivation given in Ref. [32]) , the master equation in the Pauli form can be obtained as…”

“…where the instantaneous emission rate is neglected compared to k field , which is the optical induced transition rate tunable with the light intensity [32].…”

“…When the lead-molecule coupling is weak, the most efficient approach is to exploit quantum master equations [28,29,30]. The effect of the resonant light is included into the master equation by considering a transition rate between ground and excited states, whose magnitude is proportional to the light intensity [31,32]. In most of theoretical studies the effect of triplet states are ignored due to the small triplet-singlet transition rate [33,29,34].…”

“…In most of theoretical studies the effect of triplet states are ignored due to the small triplet-singlet transition rate [33,29,34]. However, it was shown that the triplet states cannot be ignored in the studying the optical response of the molecular junctions, as even though the direct singlet-triplet transition is impossible, one can adjust the parameters in such a way to have the indirect transition through the charged states [31,32].…”