Abstract
We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode.
Highlights
The Anderson–Holstein model is widely used to describe electronic transport through individual molecules contacted between two leads: the lowest unoccupied molecular orbital is described as a single, spin-degenerate level of a quantum dot with a Coulomb repulsion between electrons of opposite spin
We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group
We have studied the spectral and transport properties of the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG)
Summary
The Anderson–Holstein model is widely used to describe electronic transport through individual molecules contacted between two leads: the lowest unoccupied molecular orbital is described as a single, spin-degenerate (in the absence of a magnetic field) level of a quantum dot with a Coulomb repulsion between electrons of opposite spin. Equilibrium properties, such as linear conductance and spectral density, of the Anderson–Holstein model have been studied perturbatively [1, 2], and non-perturbatively using numerical renormalization group (NRG) techniques [3, 4]. Going beyond the STM-like setup the Anderson–Holstein model in a bias voltage driven non-equilibrium steady-state has been studied using real-time diagrammatics [7], rate equations [1, 8, 9] and slave-boson techniques [10, 11] In these cases the double occupation of the dot has been forbidden by considering the limit of an infinitely strong Coulomb repulsion, suppressing all charge fluctuations.
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