Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid.

The paradigm of Landau's Fermi liquid theory has been challenged with the finding of a strongly interacting Fermi liquid that cannot be adiabatically connected to a non-interacting system. A spin-1 two-channel Kondo impurity with anisotropy D has a quantum phase transition between two topologically different Fermi liquids with a peak (dip) in the Fermi level for D < Dc (D > Dc). Extending this theory to general multi-orbital problems with finite magnetic field, we reinterpret in a unified and consistent fashion several experimental studies of iron phthalocyanine molecules on Au(111) that were previously described in disconnected and conflicting ways. The differential conductance shows a zero-bias dip that widens when the molecule is lifted from the surface (reducing the Kondo couplings) and is transformed continuously into a peak under an applied magnetic field. We reproduce all features and propose an experiment to induce the topological transition.

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.

Tomography of Zero-Energy End Modes in Topological Superconducting Wires.

We describe the Majorana zero modes in topological hybrid superconductor-semiconductor wires with spin-orbit coupling and magnetic field, in terms of generalized Bloch coordinates φ,θ,δ. When the spin-orbit coupling and the magnetic field are perpendicular, φ and δ are universal in an appropriate coordinate system. We show how to extract the angle θ from the behavior of the Josephson current-phase relation, which enables tomography of the Majorana modes. Simple analytical expressions describe accurately the numerical results.

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.

Ginzburg-Landau theory for the magnetic and structural transitions in La1-y (Ca1-x Sr x ) y MnO3.

We present a phenomenological theory for the ferromagnetic transition temperature, the magnetic susceptibility at high temperatures, and the structural distortion in the La[Formula: see text](Ca[Formula: see text]Sr[Formula: see text])[Formula: see text]MnO[Formula: see text] system. We construct a Ginzburg-Landau free energy that describes the magnetic and the structural transitions, and a competition between them. The parameters of the magnetic part of the free energy are derived from a mean-field solution of the magnetic interaction for arbitrary angular momentum. The theory provides a qualitative description of the observed magnetic and structural phase transitions as functions of Sr-doping level ([Formula: see text]) for [Formula: see text].

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.

Generalized One-Band Model Based on Zhang-Rice Singlets for Tetragonal CuO.

Tetragonal CuO (T-CuO) has attracted attention because of its structure similar to that of the cuprates. It has been recently proposed as a compound whose study can give an end to the long debate about the proper microscopic modeling for cuprates. In this work, we rigorously derive an effective one-band generalized t-J model for T-CuO, based on orthogonalized Zhang-Rice singlets, and make an estimative calculation of its parameters, based on previous ab initio calculations. By means of the self-consistent Born approximation, we then evaluate the spectral function and the quasiparticle dispersion for a single hole doped in antiferromagnetically ordered half filled T-CuO. Our predictions show very good agreement with angle-resolved photoemission spectra and with theoretical multiband results. We conclude that a generalized t-J model remains the minimal Hamiltonian for a correct description of single-hole dynamics in cuprates.

Leading temperature dependence of the conductance in Kondo-correlated quantum dots.

Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

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.

Interpretation of experimental results on Kondo systems with crystal field.

We present a simple approach to calculate the thermodynamic properties of single Kondo impurities including orbital degeneracy and crystal field effects (CFE) by extending a previous proposal by Schotte and Schotte (1975 Phys. Lett. 55A 38). Comparison with exact solutions for the specific heat of a quartet ground state split into two doublets shows deviations below 10% in the absence of CFE and a quantitative agreement for moderate or large CFE. As an application, we fit the measured specific heat of the compounds CeCu2Ge2, CePd3Si0.3, CePdAl, CePt, Yb2Pd2Sn and YbCo2Zn20. The agreement between theory and experiment is very good or excellent depending on the compound, except at very low temperatures due to the presence of magnetic correlations (not accounted for in the model).

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 conductance of a nanodevice for small bias voltage.

Using nonequilibrium renormalized perturbation theory, we calculate the retarded and lesser self-energies, the spectral density ρ(ω) near the Fermi energy, and the conductance G through a quantum dot as a function of a small bias voltage V, in the general case of electron-hole asymmetry and intermediate valence. The linear terms in ω and V are given exactly in terms of thermodynamic quantities. When the energies necessary to add the first electron (Ed) and the second one (Ed + U) to the quantum dot are not symmetrically placed around the Fermi level, G has a term linear in V if, in addition, either the voltage drop or the coupling to the leads is not symmetric. The effects of temperature are discussed. The results simplify for a symmetric voltage drop, a situation usual in experiment.

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.

Spin-spin indirect interaction at low-energy excitation in zero-dimensional cavities.

We solve the low-energy part of the spectrum of a model that describes a circularly polarized cavity mode strongly coupled to two exciton modes, each of which is coupled to a localized spin of arbitrary magnitude. In the regime in which the excitons and the cavity modes are strongly coupled, forming polaritons, the low-energy part of the spectrum can be described by an effective spin model, which contains a magnetic field, an axial anisotropy, and an Ising interaction between the localized spins. For detunings such that the low-energy states are dominated by nearly degenerate excitonic modes, the description of the low-energy states by a simple effective Hamiltonian ceases to be valid and the effective interaction tends to vanish. Finally, we discuss a possible application to two-qubit quantum computing operations in a system of transition-metal impurities embedded in quantum dots inside a micropillar.

Mechanical control of spin states in spin-1 molecules and the underscreened Kondo effect.

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 stretched 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 only partially compensate the molecular spin. Our findings demonstrate a mechanism of spin control in single-molecule devices and establish that they can serve as model systems for making precision tests of correlated-electron theories.

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.

Photoluminescence of a quantum dot hybridized with a continuum of extended states.

We calculate the intensity of photon emission from a trion in a single quantum dot, as a function of energy and gate voltage, using the impurity Anderson model and variational wave functions. Assuming a flat density of conduction states and constant hybridization energy, the results agree with the main features observed in recent experiments: nonmonotonic dependence of the energy on gate voltage, non-Lorentzian line shapes, and a linewidth that increases near the regions of instability of the single electron final state to occupations zero or two.

Dynamical mean field theory of an effective three-band model for NaxCoO2.

We derive an effective Hamiltonian for highly correlated t_{2g} states centered at the Co sites of NaxCoO2. The essential ingredients of the model are an O mediated hopping, a trigonal crystal-field splitting, and on-site effective interactions derived from the exact solution of a multiorbital model in a CoO6 cluster, with parameters determined previously. The effective model is solved by dynamical mean field theory. We obtain a Fermi surface and electronic dispersion that agrees well with angle-resolved photoemission spectra. Our results also elucidate the origin of the "sinking pockets" in different doping regimes.