# 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

## TL;DR

This paper extends a theoretical model to study how electron-phonon interactions and vibrational relaxation affect photoinduced anomalous Coulomb blockade in molecular transistors, revealing new photocurrent mechanisms due to these couplings.

## Contribution

It introduces a generalized master equation approach using Redfield theory to analyze the effects of electron-phonon coupling and vibrational relaxation on Coulomb blockade phenomena.

## Key findings

- Identification of a new photocurrent mechanism due to electron-phonon coupling.
- Analytical formulas for photoinduced current in different vibrational regimes.
- Predictions of observable photoinduced Coulomb blockade effects in experiments.

## Abstract

We generalize our previous theory [Nano Lett. \textbf{18}, 5015-5023 (2018)] to investigate the influence of electron-phonon (e-p) coupling and vibrational relaxation on photoinduced \textit{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.