Many-Body Effects on the Transport Properties of Single-Molecule Devices

Abstract

The conductance through a molecular device including electron-electron and electron-phonon interactions is calculated using the numerical renormalization group method. At low temperatures and weak electron-phonon coupling the properties of the conductance can be explained in terms of the standard Kondo model with renormalized parameters. At large electron-phonon coupling a charge analog of the Kondo effect takes place that can be mapped into an anisotropic Kondo model. In this regime the molecule is strongly polarized by a gate voltage which leads to rectification in the current-voltage characteristics of the molecular junction.

Effects of electron-phonon coupling in the Kondo regime of a two-orbital molecule

“…This phenomenon is known from the Anderson-Holstein model (e.g., see Ref. 50) to arise from the small overlap between the bosonic ground state of the displaced oscillator that minimizes the energy in the sectors n mol = 0 and the corresponding ground state for n mol = 2. This small overlap leads to an exponential reduction in the effective value of the level width Γ in the regime of negative effective U.…”

“…[39][40][41][42][43][44][45][46][47][48][49][50][51] It is well-established for this model that the ratio ω 0 /Γ is a key quantity governing the interplay between e-ph interactions and the Kondo effect. In the instantaneous or anti-adiabatic regime ω 0 ≫ Γ, the bosons adjust rapidly to any change in the orbital occupancy, leading to polaronic shifts in the orbital energy and in the Coulomb interaction and to exponential suppression of certain virtual tunneling processes.…”

“…Variants of the model have been studied since the 1970s in connection with other problems [39][40][41][42][43][44][45][46][47][48][49] prior to their application to singlemolecule devices. [50][51][52][53][54][55][56][57][58][59] Various analytical approximations as well as nonperturbative numerical renormalization-group calculations have shown that in equilibrium, the Holstein coupling reduces the Coulomb repulsion between two electrons in the impurity level, even yielding effective e-e attraction for sufficiently strong e-ph coupling. Increasing the e-ph coupling from zero can produce a smooth crossover from a conventional Kondo effect, involving conduction-band screening of the impurity spin degree of freedom, to a charge Kondo effect in which it is the impurity "isospin" or deviation from halffilling that is quenched by the conduction band.…”

Slave boson theory for transport through magnetic molecules with vibronic states

“…This naturally leads to an increase of the Kondo temperature while it reduces the range of gate voltages where the charge state with one electron is stable. 19 For large enough λ , U becomes negative, which corresponds to an electronphonon induced attractive interaction. In what follows we consider the case U > 0.…”

“…As the Coulomb charging energies in these systems can be considerably reduced by screening due to the electrodes, 14 electronic and vibrational energies can become of the same order of magnitude generating scenarios where novel effects may emerge. 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32 The effect of the coupling between electronic excitations and vibronic states in molecular transistors depends on the symmetry and frequency of the vibrating mode and on the strength of the coupling. Symmetric modes with a Holstein coupling between quantized vibrations and electronic levels may strongly renormalize the molecular parameters reducing charging energies 15 and producing anomalous behavior of the Kondo temperature versus applied gate voltages.…”