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To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variational Lang-Firsov transformation, combined with a perturbative calculation of the electron-phonon self-energy in the framework of generalised Matsubara functions. This allows us to describe the system at weak to strong coupling and intermediate to large phonon frequencies. We present results for the quantum dot spectral function and for the kinetic coefficient that characterises the electron transport through the dot. With these results we critically examine the strengths and limitations of our approach, and discuss the properties of the molecular quantum dot in the context of polaron physics. We place particular emphasis on the importance of corrections to the concept of an antiadiabatic dot polaron suggested by the complete Lang-Firsov transformation.
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We consider transport through a vibrating molecular quantum dot contacted to macroscopic leads acting as charge reservoirs. In the equilibrium and nonequilibrium regime, we study the formation of a polaron-like transient state at the quantum dot for all ratios of the dot-lead coupling to the energy of the local phonon mode. We show that the polaronic renormalization of the dot-lead coupling is a possible mechanism for negative differential conductance. Moreover, the effective dot level follows one of the lead chemical potentials to enhance resonant transport, causing novel features in the inelastic tunneling signal. In the linear response regime, we investigate the impact of the electron-phonon interaction on the thermoelectrical properties of the quantum dot device.
We investigate the effect of vibrational degrees of freedom on the linear thermoelectric transport through a single-level quantum dot described by the spinless Anderson-Holstein impurity model. To study the effects of strong electron-phonon coupling, we use the nonperturbative numerical renormalization group approach. We also compare our results, at weak to intermediate coupling, with those obtained by employing the functional renormalization group method, finding good agreement in this parameter regime. When applying a gate voltage at finite temperatures, the inelastic scattering processes, induced by phonon-assisted tunneling, result in an interesting interplay between electrical and thermal transport. We explore different parameter regimes and identify situations for which the thermoelectric power as well as the dimensionless figure of merit are significantly enhanced via a Mahan-Sofo type of mechanism. We show, in particular, that this occurs at strong electron-phonon coupling and in the antiadiabatic regime.
We employ the functional renormalization group to study the effects of phonon-assisted tunneling on the nonequilibrium steady-state transport through a single level molecular quantum dot coupled to electronic leads. Within the framework of the spinless Anderson-Holstein model, we focus on small to intermediate electron-phonon couplings, and we explore the evolution from the adiabatic to the antiadiabatic limit and also from the low-temperature non-perturbative regime to the high temperature perturbative one. We identify the phononic signatures in the bias-voltage dependence of the electrical current and the differential conductance. Considering a temperature gradient between the electronic leads, we further investigate the interplay between the transport of charge and heat. Within the linear response regime, we compare the temperature dependence of various thermoelectric coefficients to our earlier results obtained within the numerical renormalization group [Phys.~Rev.~B {bf 96}, 195156 (2017)]. Beyond the linear response regime, in the context of thermoelectric generators, we discuss the influence of molecular vibrations on the output power and the efficiency. We find that the molecular energy dissipation, which is inevitable in the presence of phonons, is significantly suppressed in the antiadiabatic limit resulting in the enhancement of the thermoelectric efficiency.
The transmission of electrons through a non-interacting tight-binding chain with an interacting side quantum dot (QD) is analized. When the Kondo effect develops at the dot the conductance presents a wide minimum, reaching zero at the unitary limit. This result is compared to the opposite behaviour found in an embedded QD. Application of a magnetic field destroys the Kondo effect and the conductance shows pairs of dips separated by the charging energy U. The results are discussed in terms of Fano antiresonances and explain qualitatively recent experimental results.
We analyze the electronic transport through a model spin-1 molecule as a function of temperature, magnetic field and bias voltage. We consider the effect of magnetic anisotropy, which can be generated experimentally by stretching the molecule. In the experimentally relevant regime the conductance of the unstretched molecule reaches the unitary limit of the underscreened spin- 1 Kondo effect at low temperatures. The magnetic anisotropy generates an antiferromagnetic coupling between the remaining spin 1/2 and a singular density of quasiparticles, producing a second Kondo effect and a reduced conductance. The results explain recent measurements in spin-1 molecules [Science 328 1370 (2010)].
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