Non-equilibrium conductance through a benzene molecule in the Kondo regime

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. When the leads are connected in the para position (at 180°), the model is equivalent to the ordinary impurity Anderson model and its known properties are recovered. For other positions, there is a partial destructive interference in the co-tunneling processes involving the two doublets and, as a consequence, the Kondo temperature and the height and width of the central peak (for bias voltage V(b) near zero) of the differential conductance G = dI/dV(b) (where I is the current) are reduced. In addition, two peaks at finite V(b) appear. We study the position of these peaks, the temperature dependence of G and the spectral densities. Our formalism can also be applied to carbon nanotube quantum dots with intervalley mixing.

Symmetry-driven novel Kondo effect in a molecule

The Kondo effect caused by the adsorption of iron phthalocyanine (FePc) on Au(111) was investigated by the combination of density functional theory and a numerical renormalization group calculation with scanning tunneling microscopy. We found that a novel Kondo effect is realized for a single FePc molecule on Au(111) by tuning the symmetry of the ligand field through the local coordination to the substrate. For FePc in the on top configuration where fourfold symmetry around the Fe(2+) ion is held, the orbital degrees of freedom survive, resulting in the spin+orbital SU(4) Kondo effect. In contrast, the reduced symmetry in the bridge configuration freezes the orbital degrees of freedom, leading to the spin SU(2) Kondo effect. These results provide a novel example to manipulate the many-body phenomena by tuning the local symmetry.

Spin doping of individual molecules by using single-atom manipulation

Being able to control the spin of magnetic molecules at the single-molecule level will make it possible to develop new spin-based nanotechnologies. Gate-field effects and electron and photon excitations have been used to achieve spin switching in molecules. Here, we show that atomic doping of molecules can be used to change the molecular spin. Furthermore, a scanning tunneling microscope was used to place or remove the atomic dopant on the molecule, allowing us to change the molecular spin in a controlled way. Bis(phthalocyaninato)yttrium (YPc(2)) molecules deposited on an Au (111) surface keep their spin-1/2 magnetic moment due to the small molecule-substrate interaction. However, when Cs atoms were carefully placed onto YPc(2) molecules, the spin of the molecule vanished as shown by our conductance measurements and corroborated by the results of density functional theory calculations.

Conductance-driven change of the Kondo effect in a single cobalt atom

A low-temperature scanning tunneling microscope is employed to build a junction comprising a Co atom bridging a copper-coated tip and a Cu(100) surface. An Abrikosov-Suhl-Kondo resonance is evidenced in the differential conductance and its width is shown to vary exponentially with the ballistic conductance for all tips employed. Using a theoretical description based on the Anderson model, we show that the Kondo effect and the total conductance are related through the atomic relaxations affecting the environment of the Co atom.

Kondo effect of magnetic impurities in nanotubes

Transition metal impurities will yield zero-bias anomalies in the conductance of well contacted metallic carbon nanotubes, but Kondo temperatures and geometry dependences have not been anticipated so far. Applying the density functional plus numerical renormalization group approach of Lucignano et al. to Co and Fe impurities in (4,4) and (8,8) nanotubes, we discover a huge difference of behavior between outside versus inside adsorption of the impurity. The predicted Kondo temperatures and zero-bias anomalies, tiny outside the nanotube, turn large and strongly radius dependent inside, owing to a change of symmetry of the magnetic orbital. Observation of this Kondo effect should open the way to a host of future experiments.

Ground state of the parallel double quantum dot system

We resolve the controversy regarding the ground state of the parallel double quantum dot system near half filling. The numerical renormalization group predicts an underscreened Kondo state with residual spin-1/2 magnetic moment, ln2 residual impurity entropy, and unitary conductance, while the Bethe ansatz solution predicts a fully screened impurity, regular Fermi-liquid ground state, and zero conductance. We calculate the impurity entropy of the system as a function of the temperature using the hybridization-expansion continuous-time quantum Monte Carlo technique, which is a numerically exact stochastic method, and find excellent agreement with the numerical renormalization group results. We show that the origin of the unconventional behavior in this model is the odd-symmetry "dark state" on the dots.

Unconventional Kondo effect in redox active single organic macrocyclic transistors

Cyclo[6]- and cyclo[8]pyrrole, two aromatic expanded porphyrins, were studied in a single-molecule transistor (SMT) setup. The analyses of these compounds allowed us to observe an uncommon absence of an even-odd effect in the Kondo resonance in discrete, metal-free organic macrocyclic compounds. The findings from the SMT measurements of these cyclopyrroles were in accord with those from cyclic voltammetry (CV) studies and theoretical analyses. These findings provide support for the notion that SMT measurements could be useful as a tool for the characterization of similar types of aromatic macrocyclic compounds.

Mechanically controlled molecular orbital alignment in single molecule junctions

Research in molecular electronics often involves the demonstration of devices that are analogous to conventional semiconductor devices, such as transistors and diodes, but it is also possible to perform experiments that have no parallels in conventional electronics. For example, by applying a mechanical force to a molecule bridged between two electrodes, a device known as a molecular junction, it is possible to exploit the interplay between the electrical and mechanical properties of the molecule to control charge transport through the junction. 1,4'-Benzenedithiol is the most widely studied molecule in molecular electronics, and it was shown recently that the molecular orbitals can be gated by an applied electric field. Here, we report how the electromechanical properties of a 1,4'-benzenedithiol molecular junction change as the junction is stretched and compressed. Counterintuitively, the conductance increases by more than an order of magnitude during stretching, and then decreases again as the junction is compressed. Based on simultaneously recorded current-voltage and conductance-voltage characteristics, and inelastic electron tunnelling spectroscopy, we attribute this finding to a strain-induced shift of the highest occupied molecular orbital towards the Fermi level of the electrodes, leading to a resonant enhancement of the conductance. These results, which are in agreement with the predictions of theoretical models, also clarify the origins of the long-standing discrepancy between the calculated and measured conductance values of 1,4'-benzenedithiol, which often differ by orders of magnitude.

Interaction of spin and vibrations in transport through single-molecule magnets

We study electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. Based on numerical renormalization group calculations 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.

Spin coupling and relaxation inside molecule-metal contacts

Advances in molecular electronics depend on the ability to control the charge and spin of single molecules at the interface with a metal. Here we show that bonding of metal-organic complexes to a metallic substrate induces the formation of coupled metal-ligand spin states, increasing the spin degeneracy of the molecules and opening multiple spin relaxation channels. Scanning tunnelling spectroscopy reveals the sign and magnitude of intramolecular exchange coupling as well as the orbital character of the spin-polarized molecular states. We observe coexisting Kondo, spin, and vibrational inelastic channels in a single molecule, which lead to pronounced intramolecular variations of the conductance and spin dynamics. The spin degeneracy of the molecules can be controlled by artificially fabricating molecular clusters of different size and shape. By comparing data for vibronic and spin-exchange excitations, we provide a positive test of the universal scaling properties of inelastic Kondo processes having different physical origin.

Orbital Kondo effect in cobalt-benzene sandwich molecules

We study a Co-benzene sandwich molecule bridging the tips of a Cu nanocontact as a realistic model of correlated molecular transport. To this end we employ a recently developed method for calculating the correlated electronic structure and transport properties of nanoscopic conductors. When the molecule is slightly compressed by the tips of the nanocontact the dynamic correlations originating from the strongly interacting Co 3d shell give rise to an orbital Kondo effect while the usual spin Kondo effect is suppressed due to Hund's rule coupling. This nontrivial Kondo effect produces a sharp and temperature-dependent Abrikosov-Suhl resonance in the spectral function at the Fermi level and a corresponding Fano line shape in the low bias conductance.

Transport and accumulation of spin anisotropy

We show that spin anisotropy can be transferred to an isotropic system by transport of a spin-quadrupole moment. We derive the quadrupole moment current and continuity equation and study a spin-valve structure consisting of two ferromagnets coupled to a quantum dot probing an impurity spin. The quadrupole backaction on their coupled spin results in spin torques and anisotropic spin relaxation which do not follow from standard spin-current considerations. We demonstrate the detection of the impurity spin by charge transport and its manipulation by electric fields.

Real-space imaging of Kondo screening in a two-dimensional O₂ lattice

Kondo lattice systems can exhibit unusual many-body behaviors that result from the interplay between onsite Kondo screening and intersite coupling. We used scanning tunneling microscopy to image the Kondo resonance in a nonconventional Kondo lattice formed by self-assembled oxygen (O(2)) molecules, which are paramagnetic, on the gold reconstructed surface [Au(110)-1×2]. The interplay between the intermolecular coupling for molecules adsorbed along chains and the onsite Kondo effect leads to the coexistence of both local and nonlocal Kondo screening at the atomic level. The latter provides evidence for collective deconfinement of magnetization induced in Au, whereas the former shows local "hybridization" between the Kondo clouds of nearest-neighbor O(2) molecules.

Dependence of single-molecule conductance on molecule junction symmetry

The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.

Conductance histogram evolution of an EC-MCBJ fabricated Au atomic point contact

This work presents a study of Au conductance quantization based on a combined electrochemical deposition and mechanically controllable break junction (MCBJ) method. We describe the microfabrication process and discuss improved features of our microchip structure compared to the previous one. The improved structure prolongs the available life of the microchip and also increases the success rate of the MCBJ experiment. Stepwise changes in the current were observed at the last stage of atomic point contact breakdown and conductance histograms were constructed. The evolution of 1G0 peak height in conductance histograms was used to investigate the probability of formation of an atomic point contact. It has been shown that the success rate in forming an atomic point contact can be improved by decreasing the stretching speed and the degree that the two electrodes are brought into contact. The repeated breakdown and formation over thousands of cycles led to a distinctive increase of 1G0 peak height in the conductance histograms, and this increased probability of forming a single atomic point contact is discussed.

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund's rule, underscreened Kondo effect and quantum phase transitions

We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dot experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generally asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows fine-tuning with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically 'ordered' state. These observations are put theoretically into a consistent global picture by using new numerical renormalization group simulations, tailored to capture sharp finite-voltage cotunneling features within the Coulomb diamonds, together with complementary out-of-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.

Competition of superconducting phenomena and Kondo screening at the nanoscale

Magnetic and superconducting interactions couple electrons together to form complex states of matter. We show that, at the atomic scale, both types of interactions can coexist and compete to influence the ground state of a localized magnetic moment. Local spectroscopy at 4.5 kelvin shows that the spin-1 system formed by manganese-phthalocyanine (MnPc) adsorbed on Pb(111) can lie in two different magnetic ground states. These are determined by the balance between Kondo screening and superconducting pair-breaking interactions. Both ground states alternate at nanometer length scales to form a Moiré-like superstructure. The quantum phase transition connecting the two (singlet and doublet) ground states is thus tuned by small changes in the molecule-lead interaction.

Bond Tension in Tethered Macromolecules

The paper presents scaling analysis of mechanical tension generated in densely branched macromolecules tethered to a solid substrate with a short linker. Steric repulsion between branches results in z-fold amplification of tension in the linker, where z is the number of chain-like arms. At large z ~ 100-1000, the generated tension may exceed the strength of covalent bonds and sever the linker. Two types of molecular architectures were considered: polymer stars and polymer "bottlebrushes" tethered to a solid substrate. Depending on the grafting density, one distinguishes the so-called mushroom, loose grafting, and dense grafting regimes. In isolated (mushroom) and loosely tethered bottlebrushes, the linker tension is by a factor of [Formula: see text] smaller than the tension in a tethered star with the same number of arms z. In densely tethered stars, the effect of interchain distance (d) and number of arms (z) on the magnitude of linker tension is given by f ≅ f₀z^3/2(b/d) for stars in a solvent environment and f ≅ f₀z² (b/d)² for dry stars, where b is the Kuhn length and f₀ ≅ k_BT/b is intrinsic bond tension. These relations are also valid for tethered bottlebrushes with long side chains. However, unlike molecular stars, bottlebrushes demonstrate variation of tension along the backbone f ≅ f₀s z^1/2 / d as a function of distance s from the free end of the backbone. In dense brushes [Formula: see text] with z ≅ 1000, the backbone tension increases from f ≅ f₀ = 1 pN at the free end of the backbone (s ≅ b) to its maximum f ≅ zf₀ ≅ 1 nN at the linker to the substrate (s ≅ zb).

Interplay of the Kondo effect and spin-polarized transport in magnetic molecules, adatoms, and quantum dots

We study the interplay of the Kondo effect and spin-polarized tunneling in a class of systems exhibiting uniaxial magnetic anisotropy. 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 strength of exchange coupling and on the anisotropy constant.

Controlling the interparticle distance in a 2D molecule-nanoparticle network

Mechanically controllable break junctions allow for an impressive level of control over the distance between two electrodes, but lack stability at room temperature. On the other hand, two-dimensional (2D) networks of nanoparticles bridged by molecules form a stable device structure for investigating molecular conductance properties. Here, we combine both techniques to create a robust platform for molecular charge transport with control over the inter-electrode distance on the picometer scale. The resistance change due to bending of our structures is dependent on the molecular species present between the nanoparticles.

Quantum tunnelling of the magnetization in a monolayer of oriented single-molecule magnets

A fundamental step towards atomic- or molecular-scale spintronic devices has recently been made by demonstrating that the spin of an individual atom deposited on a surface, or of a small paramagnetic molecule embedded in a nanojunction, can be externally controlled. An appealing next step is the extension of such a capability to the field of information storage, by taking advantage of the magnetic bistability and rich quantum behaviour of single-molecule magnets (SMMs). Recently, a proof of concept that the magnetic memory effect is retained when SMMs are chemically anchored to a metallic surface was provided. However, control of the nanoscale organization of these complex systems is required for SMMs to be integrated into molecular spintronic devices. Here we show that a preferential orientation of Fe(4) complexes on a gold surface can be achieved by chemical tailoring. As a result, the most striking quantum feature of SMMs-their stepped hysteresis loop, which results from resonant quantum tunnelling of the magnetization-can be clearly detected using synchrotron-based spectroscopic techniques. With the aid of multiple theoretical approaches, we relate the angular dependence of the quantum tunnelling resonances to the adsorption geometry, and demonstrate that molecules predominantly lie with their easy axes close to the surface normal. Our findings prove that the quantum spin dynamics can be observed in SMMs chemically grafted to surfaces, and offer a tool to reveal the organization of matter at the nanoscale.

A single molecule Kondo switch: multistability of tetracyanoethylene on Cu(111)

Single tetracyanoethyelene (TCNE) molecules on Cu(111) are reversibly switched among five states by applying voltage pulses with the tip of a scanning tunneling microscope. A pronounced Kondo resonance in tunneling spectroscopy indicates that one of the states is magnetic. Side bands of the Kondo resonance appear at energies which correspond to inter- and intramolecular vibrational modes. Density functional theory suggests that molecular deformation changes the occupancy in TCNE's molecular orbitals, thus producing the magnetic state.

Kondo resonances in molecular devices

Molecular electronic devices currently serve as a platform for studying a variety of physical phenomena only accessible at the nanometer scale. One such phenomenon is the highly correlated electronic state responsible for the Kondo effect, manifested here as a "Kondo resonance" in the conductance. Because the Kondo effect results from strong electron-electron interactions, it is not captured by the usual quantum chemistry approaches traditionally applied to understand chemical electron transfer. In this review, we will discuss the origins and phenomenology of Kondo resonances observed in single-molecule devices, focusing primarily on the spin-1/2 Kondo state arising from a single unpaired electron. We explore the rich physical system of a single-molecule device, which offers a unique spectroscopic tool for investigating the interplay of emergent Kondo behavior and such properties as molecular orbital transitions and vibrational modes. We will additionally address more exotic systems, such as higher spin states in the Kondo regime, and we will review recent experimental advances in the ability to manipulate and exert control over these nanoscale devices.