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 the
ir hoppingto 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.
We study the role of the onset of Shockley states, $D_s$, belonging to (111) surfaces of Cu, Ag and Au in the Kondo effect when a magnetic impurity is deposited on them. When $D_s$ approaches to the Fermi level, $E_F$, thing that can be done by compr
essing (stretching) the metallic sample, we found that most of the thermodynamic and dynamic properties of the impurity are affected in a non trivial way. We model the system by a generic Anderson impurity model and solve it by using the numerical renormalization group, NRG, technique. In particular, the impurity contribution to magnetic susceptibility and entropy as a function of temperature exhibit negative values and goes to zero slowly in a logarithmic shape. Furthermore, we found a suppression of the spectral density weight at the Fermi level when $D_ssim E_F$ even in the Kondo regime. As a consequence, the conductance through the impurity is strongly reduced by near $25%$ of the unitary value $2e^2/h$. Finally, we analyze these features in realistic systems like Co on Ag(111) reported in the literature.
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 conduct
ance 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.
We study the thermoelectric response of a device containing a pair of helical edge states contacted at the same temperature $T$ and chemical potential $mu$ and connected to an external reservoir, with different chemical potential and temperature, thr
ough a side quantum dot. Different operational modes can be induced by applying a magnetic field $B$ and a gate voltage $V_g$ at the quantum dot. At finite $B$, the quantum dot acts simultaneously as a charge and a spin filter. Charge and spin currents are induced, not only through the quantum dot, but also along the edge states. We focus on linear response and analyze the regimes, which we identify as charge heat engines or refrigerator, spin heat engine and spin refrigerator.
Using a combination of scanning tunneling spectroscopy and atomic lateral manipulation, we obtained a systematic variation of the Kondo temperature ($T_mathrm K$) of Co atoms on Ag(111) as a function of the surface state contribution to the total den
sity of states at the atom adsorption site ($rho_s$). By sampling the $T_mathrm K$ of a Co atom on positions where $rho_s$ was spatially resolved beforehand, we obtain a nearly linear relationship between both magnitudes. We interpret the data on the basis of an Anderson model including orbital and spin degrees of freedom (SU(4)) in good agreement with the experimental findings. The fact that the onset of the surface band is near the Fermi level is crucial to lead to the observed linear behavior. In the light of this model, the quantitative analysis of the experimental data evidences that at least a quarter of the coupling of Co impurities with extended states takes place through the hybridization to surface states. This result is of fundamental relevance in the understanding of Kondo screening of magnetic impurities on noble metal surfaces, where bulk and surface electronic states coexist.
We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(111), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one h
ole at the $3d_{z^2}$ orbital of iron and two degenerate doublets corresponding to one hole either in the $3d_{xz}$ or in the $3d_{yz}$ orbital (called $pi$ orbitals) with two degenerate Hund-rule triplets with one hole in the $3d_{z}$ orbital and another one in a $pi$ 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 stage takes place in two stages, with different energy scales $T_K^z > T_K^pi$ corresponding to the Kondo temperatures related with the hopping of the $z^2$ and $pi$ 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.
We calculate the width $2Delta_{text{CT}}$ and intensity of the charge-transfer peak (the one lying at the on-site energy $E_d$) in the impurity spectral density of states as a function of $E_d$ in the SU($N$) impurity Anderson model (IAM). We use th
e dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for $N$=4, and a 1/$N$ variational approximation in the general case. In particular, while for $E_d gg Delta$, where $Delta$ is the resonant level half-width, $Delta_{text{CT}}=Delta$ as expected in the noninteracting case, for $-E_d gg N Delta$ one has $Delta_{text{CT}}=NDelta$. In the $N$=2 case, some effects of the variation of $% Delta_{text{CT}}$ with $E_d$ were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. Konemann textit{et al.}, Phys. Rev. B textbf{73}, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.
The (111) surface of Cu, Ag and Au is characterized by a band of surface Shockley states, with constant density of states beginning slightly below the Fermi energy. These states as well as bulk states hybridize with magnetic impurities which can be p
laced above the surface. We calculate the characteristic low-temperature energy scale, the Kondo temperature $T_K$ of the impurity Anderson model, as the bottom of the conduction band $D_s$ crosses the Fermi energy $epsilon_F$. We find simple power laws $T_K simeq |D_s-epsilon_F|^{eta}$, where $eta$ depends on the sign of $D_s-epsilon_F$, the ratio between surface and bulk hybridizations with the impurity $Delta_s/Delta_b$ and the ratio between on-site and Coulomb energy $E_d/U$ in the model.
The low temperature properties of single level molecular quantum dots including both, electron-electron and electron-vibration interactions, are theoretically investigated. The calculated differential conductance in the Kondo regime exhibits not only
the zero bias anomaly but also side peaks located at bias voltages which coincide with multiples of the energy of vibronic mode $V sim hbarOmega/e$. We obtain that the evolution with temperature of the two main satellite conductance peaks follows the corresponding one of the Kondo peak when $hbarOmega gg k_B T_K$, being $ T_K$ the Kondo temperature, in agreement with recent transport measurements in molecular junctions. However, we find that this is no longer valid when $ hbarOmega$ is of the order of a few times $k_B T_K$.
By means of ab initio calculations we study the effect of O-doping of Au chains containing a nanocontact represented by a Ni atom as a magnetic impurity. In contrast to pure Au chains, we find that with a minimun O-doping the $5d_{xz,yz}$ states of A
u are pushed up, crossing the Fermi level. We also find that for certain O configurations, the Ni atom has two holes in the degenerate $3d_{xz,yz}$ orbitals, forming a spin $S=1$ due to a large Hund interaction. The coupling between the $5d_{xz,yz}$ Au bands and the $3d_{xz,yz}$ of Ni states leads to a possible realization of a two-channel $S=1$ Kondo effect. While this kind of Kondo effect is commonly found in bulk systems, it is rarely observed in low dimensions. The estimated Kondo scale of the system lies within the present achievable experimental resolution in transport measurements. Another possible scenario for certain atomic configurations is that one of the holes resides in a $3d_{z^2}$ orbital, leading to a two-stage Kondo effect, the second one with SU(4) symmetry.
