We consider electronic transport through break-junctions bridged by a single molecule in the Kondo regime. We describe the system by a two-channel Anderson model. We take the tunneling matrix elements to depend on the position of the molecule. It is shown, that if the modulation of the tunneling by displacement is large, the potential confining the molecule to the central position between the leads is softened and the position of the molecule is increasingly susceptible to external perturbations that break the inversion symmetry. In this regime, the molecule is attracted to one of the leads and as a consequence the conductance is small. We argue on semi-classical grounds why the softening occurs and corroborate our findings by numerical examples obtained by Wilson's numerical renormalization group and Schoenhammer-Gunnarsson's variational method.
We show how the charge input signal applied to the gate electrode in a double and triple quantum dot may be converted to a pulse in the Kondo cotunneling current being a spin response of a nano-device under a strong Coulomb blockade. The stochastic component of the input signal results in the infrared cutoff of Kondo transmission. The stochastization of the orbital component of the Kondo effect in triple quantum dots results in a noise-induced SU(4) - SU(2) quantum transition.
Kondo effect offers an important paradigm to understand strong correlated many-body physics. Although under intensive study, some of important properties of Kondo effect, in systems where both itinerant coupling and localized coupling play significant roles, are still elusive. Here we report evolution and universality of two stage Kondo effect, the simplest form where both couplings are important using single molecule transistor devices incorporating Manganese phthalocyanine molecules. Kondo temperature T* of two-stage Kondo effect evolves linearly against effective interaction of involved two…
The site-dependent g factor of a single magnetic molecule, with intramolecular resolution, is demonstrated for the first time by low-temperature, high-magnetic-field scanning tunneling microscopy of dehydrogenated Mn-phthalocyanine molecules on Au(111). This is achieved by exploring the magneticfield dependence of the extended Kondo effect at different atomic sites of the molecule. Importantly, an inhomogeneous distribution of the g factor inside a single molecule is revealed. Our results open up a new route to access local spin properties within a single molecule.
We study numerically the low-temperature electronic transport properties of a single-ion magnet with uniaxial and transverse spin anisotropies. We find clear signatures of a Kondo effect caused by the presence of a transverse (zero-field) anisotropy in the molecule. Upon applying a transverse magnetic field to the single-ion magnet, we observe oscillations of the Kondo effect due to the presence of diabolical (degeneracy) points of the energy spectrum of the molecule caused by a geometrical phase interference effects similar to those observed in the quantum tunneling of multi-ion molecular nan…
We study the interaction between graphene and a single-molecule-magnet, [Fe4(L)2(dpm)6]. Focusing on the closest Iron ion in a hollow position with respect to the graphene sheet, we derive a channel selective tunneling Hamiltonian, that couples different d orbitals of the Iron atom to precise independent combinations of sublattice and valley degrees of freedom of the electrons in graphene. When looking at the spin-spin interaction between the molecule and the graphene electrons, close to the Dirac point the channel selectivity results in a channel decoupling of the Kondo interaction, with two …
Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111). We show that both asymmetries originate in interfering tunneling paths via a spin-carrying orbital and the highest occupied molecular orbital (HOMO). Strong evidence for th…
We study the interplay of the Kondo effect and spin-polarized tunneling in a class of systems exhibiting uniaxial magnetic anisotropy, such as magnetic molecules, magnetic adatoms, or quantum dots coupled to a single localized magnetic moment. Using the numerical renormalization group method we calculate the spectral functions and linear conductance in the Kondo regime. We show that the exchange coupling between conducting electrons and localized magnetic core generally leads to suppression of the Kondo effect. We also predict a nontrivial dependence of the tunnel magnetoresistance on the stre…
We study the Kondo temperature ($T_K$) of a single molecule break junction. By employing a numerical renormalization group calculations we have found that $T_K$ depends dramatically upon the position of the molecule in the wire formed between the contacts. We show that $T_K$ exhibits strong \emph{oscillations} when the parity of the left {and/or} right number of atomic sites ($N_L,N_R$) is changed. For a given set of parameters, the maximum value of $T_K$ occurs for ($odd,odd$) combination, while its minimum values is observed for ($even,even$). These oscillations are fully understood in terms…
Determination of the molecular Kondo temperature $T_K$ poses a challenge in most cases when the experimental temperature cannot be tuned to a sufficient extent. We show how this ambiguity can be resolved if additional control parameters are present, such as magnetic field and mechanical gating. We record the evolution of the differential conductance by lifting an individual molecule from the metal surface with the tip of a scanning tunneling microscope. By fitting the measured conductance spectra with the single impurity Anderson model we are able to demonstrate that the lifting tunes the junc…
A Kondo resonance has been observed on purely organic molecules in several combinations of charge transfer complexes on a metal surface. It has been regarded as a fingerprint of the transfer of one electron from the donor to the extended $π$ orbital of the acceptor's LUMO. Here, we investigate the stoichiometric checkerboard structure of tetrathiafulvalene (TTF) and tetracyanoethylene (TCNE) on a Au(111) surface using scanning tunneling and atomic force microscopy at 4.8 K. We find a bistable state of the TCNE molecules with distinct structural and electronic properties. The two states represe…
Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in single-molecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spin-degenerate molecule can be either enhanced or blocked by Kondo correlati…
We discuss the electronic transport through molecules in the Kondo regime. We concentrate here on the influence of molecular vibrations. Two types of vibrations are investigated: (i) the breathing internal molecular modes, where the coupling occurs between the molecular deformation and the charge density, and (ii) the oscillations of molecule between the contacts, where the displacement affects the tunneling. The system is described by models which are solved numerically using Schoenhammer-Gunnarsson's projection operators and Wilson's numerical renormalization group methods. Case (i) is consi…
Transport properties in the Kondo regime of a nanosystem displaying uniaxial magnetic anisotropy (such as a magnetic molecule, magnetic adatom or quantum dot coupled to a localized magnetic moment) are analyzed theoretically. In particular, the influence of spin-polarized transport through a local orbital of the system and exchange coupling of conduction electrons to the system's magnetic core on the Kondo effect is discussed. The numerical renormalization group method is applied to calculate the spectral functions and linear conductance in the case of the parallel and antiparallel configurati…
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 $Γ$ 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 co…
Single-ion magnetic anisotropy in molecular magnets leads to spin flip excitations that can be measured by inelastic scanning tunneling microscope (STM) spectroscopy. Here I present a semi ab initio scheme to compute the spectral features associated with inelastic spin flip excitations and Kondo effect of single molecular magnets. To this end density functional theory calculations of the molecule on the substrate are combined with more sophisticated many-body techniques for solving the Anderson impurity problem of the spin-carrying orbitals of the magnetic molecule coupled to the rest of the s…
With recent advances in the areas of nanostructure fabrication and molecular spintronics the idea of using single molecule magnets as building blocks for the next generation electronic devices becomes viable. A particular example represents a metal-organic complex in which organic ligands surround a rare-earth element or transition metal. Recently, it was explicitly shown that the relative position of the ligands with respect to each other can be reversibly changed by the external voltage without any need of the chemical modification of the sample. This opens a way of the electrical tuning of …
We report on the observation of Kondo and split Kondo peaks in single-molecule transistors containing a single spin transition molecule with a Fe2+ ion. Coulomb blockade characteristics reveal a double quantum dot behavior in a parallel configuration, making our system a molecular equivalent to a semiconducting double-quantum-dot system. As the gate voltage is increased the charging of the second dot by an additional electron induces a splitting of the Kondo peak. We discuss possible origins of this effect including a spin transition into a high-spin state.
Magnetoconductance through a vibrating molecule in the Kondo regime
利用数值重整化群方法研究了磁场对单分子结平衡态光谱和输运性质的影响。该分子由Anderson-Holstein模型描述，其中单个振动模式与电子密度耦合。在近藤体系中，外加磁场对电导的影响在弱和强电子-声子耦合体系中有着质的不同。在前一种情况下，近藤共振被分裂，电导被磁场$g mu_B B \gtrsim k_BT_K$强烈抑制，其中$T_K$是近藤温度。在强电子-声子耦合区，出现了类似于近藤效应的电荷。在这种情况下，近藤共振不分裂的领域和电导在近藤制度的$B$的值的广泛范围内增强。
Coupling between a magnetic impurity and an external bath can give rise to many-body quantum phenomena, including Kondo and Hund's impurity states in metals, and Yu-Shiba-Rusinov states in superconductors. While advances have been made in probing the magnetic properties of d-shell impurities on surfaces, the confinement of f orbitals makes them difficult to access directly. Here we show that a 4f driven Kondo resonance can be modulated spatially by asymmetric coupling between a metallic surface and a molecule containing a 4f-like moment. Strong hybridisation of dysprosium double-decker phthalo…
We study the process of production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic field modulation. When the magnetic field is resonant roughly with the molecular binding energy, Shapiro-like resonances are observed. Their resonance profiles are well fitted by the Lorentzian functions. The line widths depend on both the amplitude and the duration of the applied modulations, and are found to be dramatically broadened by thermal dephasing effect. The resonance centers shift due to both many-body effect and finite temperature effect. Our theory is consistent…
A methodology of atomically resolved Landé g factor mapping of a single molecule is reported. Mn(II)-phthalocyanine (MnPc) molecules on Au(111) surface can be dehydrogenated via atomic manipulation with manifestation of tailored extended Kondo effect, which can allow atomically resolved imaging of the Landé g factor inside a molecule for the first time. By employing dehydrogenated MnPc molecules with removal of six H atoms (-6H-MnPc) as an example, Landé g factor of atomic constituents of the molecule can be obtained, therefore offering a unique g factor mapping of single molecule. Our results…
A single molecule break junction device serves as a tunable model system for probing the many body Kondo state. The low-energy properties of this state are commonly described in terms of a Kondo model, where the response of the system to different perturbations is characterized by a single emergent energy scale, k_B*T_K. Comparisons between different experimental systems have shown issues with numerical consistency. With a new constrained analysis examining the dependence of conductance on temperature, bias, and magnetic field simultaneously, we show that these deviations can be resolved by pr…
The frequency-dependent transport through a nano-device containing a large-spin magnetic molecule is studied theoretically in the Kondo regime. Specifically, the effect of magnetic anisotropy on dynamical spin accumulation is of primary interest. Such accumulation arises due to finite off-diagonal in spin components of the dynamical conductance. Here, employing the Kubo formalism and the numerical renormalization group (NRG) method, we demonstrate that the dynamical transport properties strongly depend on magnetic configuration of the device and intrinsic parameters of the molecule. Specifical…
Scaling laws and universality are often associated with systems exhibiting emergent phenomena possessing a characteristic energy scale. We report nonequilibrium transport measurements on two different types of single-molecule transistor (SMT) devices in the Kondo regime. The conductance at low bias and temperature adheres to a scaling function characterized by two parameters. This result, analogous to that reported recently in semiconductor dots with Kondo temperatures two orders of magnitude lower, demonstrates the universality of this scaling form. We compare the extracted values of the scal…
We use a combination of first principles many-body methods and the numerical renormalization-group technique to study the Kondo regime of cobalt-porphyrin compounds adsorbed on a Cu(111) surface. We find the Kondo temperature to be highly sensitive to both molecule charging and distance to the surface, which can explain the variations observed in recent scanning tunneling spectroscopy measurements. We discuss the importance of many-body effects in the molecular electronic structure controlling this phenomenon and suggest scenarios where enhanced temperatures can be achieved in experiments.
Using a state-of-the art combination of density functional theory and impurity solver techniques we present a complete and parameter-free picture of the Kondo effect in the high-spin ($S=3/2$) coordination complex known as Manganese Phthalocyanine adsorbed on the Pb(111) surface. We calculate the correlated electronic structure and corresponding tunnel spectrum and find an asymmetric Kondo resonance, as recently observed in experiments. Contrary to previous claims, the Kondo resonance stems from only one of three possible Kondo channels with origin in the Mn 3d-orbitals, its peculiar asymmetri…
Transport through molecular magnets is studied in the regime of strong coupling to the leads. We consider a resonant-tunneling model where the electron spin in a quantum dot or molecule is coupled to an additional local, anisotropic spin via exchange interaction. The two opposite regimes dominated by resonant tunneling and by Kondo transport, respectively, are considered. In the resonant-tunneling regime, the stationary state of the impurity spin is calculated for arbitrarily strong molecule-lead coupling using a master-equation approach, which treats the exchange interaction perturbatively. W…
We theoretically investigate the transport properties of a molecule embedded in one arm of a mesoscopic Aharonov-Bohm interferometer. Due to the presence of phonons the molecule level position ($ε_d$) and the electron-electron interaction ($U$) undergo a \emph{polaronic shift} which affects dramatically the electronic transport through the molecular junction. When the electron-phonon interaction is weak the linear conductance presents Fano-line shapes as long as the direct channel between the electrodes is opened. The observed Fano resonances in the linear conductance are originated from the i…
We realize a strongly coupled double quantum dot in a single all-organic molecule by introducing a non-conjugated bridge in between two identical conjugated moieties. Spin-1/2 Kondo and Kondo enhanced low-energy excitations for respectively the odd and even electron occupation are observed in off-resonant transport. The ground state in the even occupation can be the singlet or the triplet state varying between samples. This observation suggests that both anti-ferromagnetic and ferromagnetic interactions between spins are of the same order of magnitude.
Magnetic molecules adsorbed on a superconductor give rise to a local competition of Cooper pair and Kondo singlet formation inducing subgap bound states. For Manganese-phthalocyanine molecules on a Pb(111) substrate, scanning tunneling spectroscopy resolves pairs of subgap bound states and two Kondo screening channels. We show in a combined approach of scaling and numerical renormalization group calculations that the intriguing relation between Kondo screening and superconducting pairing is solely determined by the hybridization strength with the substrate. We demonstrate that an effective one…
We study linear electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. We show that, despite the longitudinal anisotropy barrier and small transverse anisotropy, vibrational fluctuations can induce quantum spin-tunneling (QST) and a QST-Kondo effect. The interplay of spin scattering, QST and molecular vibrations can strongly enhance the Kondo effect and induce an anomalous magnetic field dependence of vibrational Kondo side-bands.
We investigate theoretically and experimentally the singlet-triplet Kondo effect induced by a magnetic field in a molecular junction. Temperature dependent conductance, $G(T)$, is calculated by the numerical renormalization group, showing a strong imprint of the relevant low energy scales, such as the Kondo temperature, exchange and singlet-triplet splitting. We demonstrate the stability of the singlet-triplet Kondo effect against weak spin anisotropy, modeled by an anisotropic exchange. Moderate spin anisotropy manifests itself by lowering the Kondo plateaus, causing the $G(T)$ to deviate fro…
The ability to make electrical contact to single molecules creates opportunities to examine fundamental processes governing electron flow on the smallest possible length scales. We report experiments in which we controllably stretch individual cobalt complexes having spin S = 1, while simultaneously measuring current flow through the molecule. The molecule's spin states and magnetic anisotropy were manipulated in the absence of a magnetic field by modification of the molecular symmetry. This control enabled quantitative studies of the underscreened Kondo effect, in which conduction electrons o…
The transport properties of a large-spin molecule strongly coupled to ferromagnetic leads in the presence of transverse magnetic anisotropy are studied theoretically. The relevant spectral functions, linear-response conductance and the tunnel magnetoresistance are calculated by means of the numerical renormalization group method. We study the dependence of transport characteristics on orbital level position, uniaxial and transverse anisotropies, external magnetic field and temperature. It is shown that while uniaxial magnetic anisotropy leads to the suppression of the Kondo effect, finite tran…
We theoretically study the nonequilibrium thermoelectric transport properties of a strongly-correlated molecule (or quantum dot) embedded in a tunnel junction. Assuming that the coupling of the molecule to the contacts is asymmetric, we determine the nonlinear current driven by the voltage and temperature gradients by using the perturbation theory. However, the subsystem consisting of the molecule strongly coupled to one of the contacts is solved by using the numerical renormalization group method, which allows for accurate description of Kondo correlations. We study the temperature gradient a…
Starting from exact eigenstates for a symmetric ring, we derive a low-energy effective generalized Anderson Hamiltonian which contains two spin doublets with opposite momenta and a singlet for the neutral molecule. For benzene, the singlet (doublets) represent the ground state of the neutral (singly charged) molecule. We calculate the non-equilibrium conductance through a benzene molecule, doped with one electron or a hole (i.e. in the Kondo regime), and connected to two conducting leads at different positions. We solve the problem using the Keldysh formalism and the non-crossing approximation…
We study the interplay between strong electron-electron and electron-phonon interactions within a two-orbital molecule coupled to metallic leads, taking into account Holstein-like coupling of a local phonon mode to the molecular charge as well as phonon-mediated interorbital tunneling. By combining canonical transformations with numerical renormalization-group calculations to address the interactions nonperturbatively and on equal footing, we obtain a comprehensive description of the system's many-body physics in the anti-adiabatic regime where the phonons adjust rapidly to changes in the orbi…
We discuss the difficulties to discover Kondo effect in the resistivity of graphene. Similarly to the Kondo effect, electron-electron interaction effects and weak localization appear as logarithmic corrections to the resistance. In order to disentangle these contributions, a refined analysis of the magnetoconductance and the magnetoresistance is introduced. We present numerical simulations which display the discrimination of both effects. Further, we present experimental data of magnetotransport. When magnetic molecules are added to graphene, a logarithmic correction to the conductance occurs,…
