Theory of Differential Conductance of Co on Cu(111) Including Co s and d Orbitals, and Surface and Bulk Cu States.

We revisit the theory of the Kondo effect observed by a scanning-tunneling microscope (STM) for transition-metal atoms (TMAs) on noble-metal surfaces, including d and s orbitals of the TMA, surface and bulk conduction states of the metal, and their hopping to the tip of the STM. Fitting the experimentally observed STM differential conductance for Co on Cu(111) including both the Kondo feature near the Fermi energy and the resonance below the surface band, we conclude that the STM senses mainly the Co s orbital and that the Kondo antiresonance is due to interference between states with electrons in the s orbital and a localized d orbital mediated by the conduction states.

Destructive quantum interference in transport through molecules with electron-electron and electron-vibration interactions.

We study the transport through a molecular junction exhibiting interference effects. We show that these effects can still be observed in the presence of molecular vibrations if Coulomb repulsion is taken into account. In the Kondo regime, the conductance of the junction can be changed by several orders of magnitude by tuning the levels of the molecule, or displacing a contact between two atoms, from nearly perfect destructive interference to values of the order of 2e 2/h expected in Kondo systems. We also show that this large conductance change is robust for reasonable temperatures and voltages for symmetric and asymmetric tunnel couplings between the source-drain electrodes and the molecular orbitals. This is relevant for the development of quantum interference effect transistors based on molecular junctions.

Two-stage three-channel Kondo physics for an FePc molecule on the Au(1 1 1) surface.

We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(1 1 1), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one hole at the [Formula: see text] orbital of iron and two degenerate doublets corresponding to one hole either in the 3d xz or in the 3d yz orbital (called π orbitals) with two degenerate Hund-rule triplets with one hole in the 3d z orbital and another one in a π orbital. We solve the model using a slave-boson mean-field approximation (SBMFA). For reasonable parameters we can describe very well the observed STS spectrum between sample bias -60 mV to 20 mV. For these parameters the Kondo effect takes place in two stages, with different energy scales [Formula: see text] corresponding to the Kondo temperatures related with the hopping of the z 2 and π orbitals respectively. There is a strong interference between the different channels and the Kondo temperatures, particularly the lowest one is strongly reduced compared with the value in the absence of the competing channel.

Reliability of the one-crossing approximation in describing the Mott transition.

We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed.

Restoring the SU(4) Kondo regime in a double quantum dot system.

We calculate the spectral density and occupations of a system of two capacitively coupled quantum dots, each one connected to its own pair of conducting leads, in a regime of parameters in which the total couplings to the leads for each dot Γ(i) are different. The system has been used recently to perform pseudospin spectroscopy by controlling independently the voltages of the four leads. For an odd number of electrons in the system, equal coupling to the leads Γ1 = Γ2, equal dot levels E1 = E2 and sufficiently large interdot repulsion U12 the system lies in the SU(4) symmetric point of spin and pseudospin degeneracy in the Kondo regime. In the more realistic case Γ1 ≠ Γ2, pseudospin degeneracy is broken and the symmetry is reduced to SU(2). Nevertheless, we find that the essential features of the SU(4) symmetric case are recovered by appropriately tuning the level difference δ = E2 - E1. After this tuning, the system behaves as an SU(4) Kondo one at low energies. Our results are relevant for experiments which look for signatures of SU(4) symmetry in the Kondo regime of similar systems.

Non-Fermi-liquid behavior in transport through Co-doped Au chains.

We calculate the conductance as a function of temperature G(T) through Au monatomic chains containing one Co atom as a magnetic impurity, and connected to two conducting leads with a fourfold symmetry axis. Using the information derived from ab initio calculations, we construct an effective model H(eff) that hybridizes a 3d(7) quadruplet at the Co site with two 3d(8) triplets through the hopping of 5d(xz) and 5d(yz) electrons of Au. The quadruplet is split by spin anisotropy due to spin-orbit coupling. Solving H(eff) with the numerical renormalization group we find that at low temperatures G(T)=a-b√[T] and the ground state impurity entropy is ln(2)/2, a behavior similar to the two-channel Kondo model. Stretching the chain leads to a non-Kondo phase, with the physics of the underscreened Kondo model at the quantum critical point.

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.

Nonequilibrium dynamics of a singlet-triplet Anderson impurity near the quantum phase transition.

We study the singlet-triplet Anderson model (STAM) in which a configuration with a doublet is hybridized with another containing a singlet and a triplet, as a minimal model to describe two-level quantum dots coupled to two metallic leads in effectively a one-channel fashion. The model has a quantum phase transition which separates regions of a doublet and a singlet ground state. The limits of integer valence of the STAM (which include a model similar to the underscreened spin-1 Kondo model) are derived and used to predict the behavior of the conductance through the system on both sides of the transition, where it jumps abruptly. At a special quantum critical line, the STAM can be mapped to an infinite- U ordinary Anderson model (OAM) plus a free spin 1/2. We use this mapping to obtain the spectral densities of the STAM as a function of those of the OAM at the transition. Using the non-crossing approximation (NCA), we calculate the spectral densities and conductance through the system as a function of temperature and bias voltage, and determine the changes that take place at the quantum phase transition. The separation of the spectral density into a singlet and a triplet part allows us to shed light on the underlying physics and to explain a shoulder observed recently in the zero bias conductance as a function of temperature in transport measurements through a single fullerene molecule (Roch et al 2008 Nature 453 633). The structure with three peaks observed in nonequilibrium transport in these experiments is also explained.