Thermoelectric effects in correlated quantum dots and molecules

We investigate thermoelectric properties of correlated quantum dots and molecules, described by a single level Anderson model coupled to conduction electron leads, by using Wilson's numerical renormalization group method. In the Kondo regime, the thermopower, $S(T)$, exhibits two sign changes, at temperatures $T=T_{1}$ and $T=T_{2}>T_{1}$. We find that $T_{2}$ is of order the level width $\Gamma$ and $T_{1}> T_{p}\approx T_{K}$, where $T_{p}$ is the position of the Kondo induced peak in the thermopower and $T_{K}$ is the Kondo scale. No sign change is found outside the Kondo regime, or, for weak correlations, making a sign change in $S(T)$ a particularly sensitive signature of strong correlations and Kondo physics. For molecules, we investigate the effect of screening by conduction electrons on the thermoelectric transport. We find that a large screening interaction enhances the figure of merit in the Kondo and mixed valence regimes.Comment: 4 pages, 3 figures; to appear in the Proceedings of the International Conference on Strongly Correlated Electron Systems, Santa Fe 2010; revised version: typos corrected and references update

Quantum phase transition in the two-band Hubbard model

The interaction between itinerant and Mott localized electronic states in strongly correlated materials is studied within dynamical mean field theory in combination with the numerical renormalization group method. A novel nonmagnetic zero temperature quantum phase transition is found in the bad-metallic orbital-selective Mott phase of the two-band Hubbard model, for values of the Hund's exchange which are relevant to typical transition metal oxides.Comment: 4 pages, 4 eps figures, revised version, to appear in Phys. Rev. Let

Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions

We develop an alternative time-dependent numerical renormalization group (TDNRG) formalism for multiple quenches and implement it to study the response of a quantum impurity system to a general pulse. Within this approach, we reduce the contribution of the NRG approximation to numerical errors in the time evolution of observables by a formulation that avoids the use of the generalized overlap matrix elements in our previous multiple-quench TDNRG formalism [Nghiem {\em et al.,} Phys. Rev. B {\bf 89}, 075118 (2014); Phys. Rev. B {\bf 90}, 035129 (2014)]. We demonstrate that the formalism yields a smaller cumulative error in the trace of the projected density matrix as a function of time and a smaller discontinuity of local observables between quenches than in our previous approach. Moreover, by increasing the switch-on time, the time between the first and last quench of the discretized pulse, the long-time limit of observables systematically converges to its expected value in the final state, i.e., the more adiabatic the switching, the more accurately is the long-time limit recovered. The present formalism can be straightforwardly extended to infinite switch-on times. We show that this yields highly accurate results for the long-time limit of both thermodynamic observables and spectral functions, and overcomes the significant errors within the single quench formalism [Anders {\em et al.}, Phys. Rev. Lett. {\bf 95}, 196801 (2005); Nghiem {\em et al.}, Phys. Rev. Lett. {\bf 119}, 156601 (2017)]. This improvement provides a first step towards an accurate description of nonequilibrium steady states of quantum impurity systems, e.g., within the scattering states NRG approach [Anders, Phys. Rev. Lett. {\bf 101}, 066804 (2008)].Comment: 15 pages and 10 figures; Additional figures and references added; typos fixed; references fixe

A brief review of recent advances on the Mott transition: unconventional transport, spectral weight transfers, and critical behaviour

Strongly correlated metals close to the Mott transition display unusual transport regimes, together with large spectral weight transfers in optics and photoemission. We briefly review the theoretical understanding of these effects, based on the dynamical mean-field theory, and emphasize the key role played by the two energy scales associated with quasiparticle coherence scale and with the Mott gap. Recent experimental results on two-dimensional organic compounds and transition metal oxides are considered in this perspective. The liquid-gas critical behaviour at the Mott critical endpoint is also discussed. Transport calculations using the numerical renormalization group are presented.Comment: Review article. 9 pages, 5 figures. Proceedings of the Vth International Conference on Crystalline Organic Metals, Superconductors and Magnets (ISCOM 2003

Nonequilibrium thermoelectric transport through vibrating molecular quantum dots

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.Comment: 11 pages, 7 figures, Published versio

Exponential and power-law renormalization in phonon-assisted tunneling

We investigate the spinless Anderson-Holstein model routinely employed to describe the basic physics of phonon-assisted tunneling in molecular devices. Our focus is on small to intermediate electron-phonon coupling; we complement a recent strong coupling study [Phys.~Rev.~B {87}, 075319 (2013)]. The entire crossover from the antiadiabatic regime to the adiabatic one is considered. Our analysis using the essentially analytical functional renormalization group approach backed-up by numerical renormalization group calculations goes beyond lowest order perturbation theory in the electron-phonon coupling. In particular, we provide an analytic expression for the effective tunneling coupling at particle-hole symmetry valid for all ratios of the bare tunnel coupling and the phonon frequency. It contains the exponential polaronic as well as the power-law renormalization; the latter can be traced back to x-ray edge-like physics. In the antiadiabatic and the adiabatic limit this expression agrees with the known ones obtained by mapping to an effective interacting resonant level model and lowest order perturbation theory, respectively. Away from particle-hole symmetry, we discuss and compare results from several approaches for the zero temperature electrical conductance of the model.Comment: 11 pages, 6 figures, Published versio

Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots

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.Comment: 14 pages, 8 figures, Published versio

Thermoelectric transport through strongly correlated quantum dots

The thermoelectric properties of strongly correlated quantum dots, described by a single level Anderson model coupled to conduction electron leads, is investigated using Wilson's numerical renormalization group method. We calculate the electronic contribution, $K_{\rm e}$, to the thermal conductance, the thermopower, $S$, and the electrical conductance, $G$, of a quantum dot as a function of both temperature, $T$, and gate voltage, ${\rm v}_g$, for strong, intermediate and weak Coulomb correlations, $U$, on the dot. For strong correlations and in the Kondo regime, we find that the thermopower exhibits two sign changes, at temperatures $T_{1}({\rm v}_g)$ and $T_{2}({\rm v}_g)$ with $T_{1}< T_{2}$. Such sign changes in $S(T)$ are particularly sensitive signatures of strong correlations and Kondo physics. The relevance of this to recent thermopower measurements of Kondo correlated quantum dots is discussed. We discuss the figure of merit, power factor and the degree of violation of the Wiedemann-Franz law in quantum dots. The extent of temperature scaling in the thermopower and thermal conductance of quantum dots in the Kondo regime is also assessed.Comment: 21 pages, 12 figures; published versio