Nonequilibrium transport through magnetic vibrating molecules

TL;DR

This paper investigates how electron-phonon coupling affects the nonequilibrium conductance in magnetic molecules or quantum dots, revealing phonon sidebands and modifications to the Kondo effect.

Contribution

It introduces a detailed theoretical analysis of the Anderson-Holstein model using Keldysh formalism and NCA, highlighting the impact of phonons on Kondo physics and conductance features.

Findings

Kondo temperature decreases moderately with electron-phonon coupling

Spectral density shows phonon satellites around the Kondo peak

Conductance exhibits peaks at multiples of phonon frequency in bias voltage

Abstract

We calculate the nonequilibrium conductance through a molecule or a quantum dot in which the occupation of the relevant electronic level is coupled with intensity $\lambda$ to a phonon mode, and also to two conducting leads. The system is described by the Anderson-Holstein Hamiltonian. We solve the problem using the Keldysh formalism and the non-crossing approximation (NCA) for both, the electron-electron and the electron-phonon interactions. We obtain a moderate decrease of the Kondo temperature $T_K$ with $\lambda$ for fixed renormalized energy of the localized level $\tilde{E_d}$. The meaning and value of $\tilde{E_d}$ are discussed. The spectral density of localized electrons shows in addition to the Kondo peak of width $2 T_K$, satellites of this peak shifted by multiples of the phonon frequency $ \omega_0$. The nonequilibrium conductance as a function of bias voltage $V_b$ at small temperatures, also displays peaks at multiples of $\omega_0$ in addition to the central dominant Kondo peak near $V_b=0$.