Universal distribution of magnetic anisotropy of impurities in ordered and disordered nano-grains

We examine the distribution of the magnetic anisotropy (MA) experienced by a magnetic impurity embedded in a metallic nano-grain. As an example of a generic magnetic impurity with partially filled $d$-shell, we study the case of $d^{1}$ impurities imbedded into ordered and disordered Au nano-grains, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by 5 real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nano-grains, these parameters exhibit symmetrical structures and reflect the symmetry of the underlying lattice, while for disordered grains they are randomly distributed and, - for stronger disorder, - their distribution is found to be characterized by random matrix theory. As a result, the probability of having small magnetic anisotropies $K_L$ is suppressed below a characteristic scale $\Delta_E$, which we predict to scale with the number of atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally

Failure of mean-field approach in out-of-equilibrium Anderson model

To explore the limitations of the mean field approximation, frequently used in \textit{ab initio} molecular electronics calculations, we study an out-of-equilibrium Anderson impurity model in a scattering formalism. We find regions in the parameter space where both magnetic and non-magnetic solutions are stable. We also observe a hysteresis in the non-equilibrium magnetization and current as a function of the applied bias voltage. The mean field method also predicts incorrectly local moment formation for large biases and a spin polarized current, and unphysical kinks appear in various physical quantities. The mean field approximation thus fails in every region where it predicts local moment formation.Comment: 5 pages, 5 figure

Low energy properties of M-state tunneling systems in metals: New candidates for non-Fermi-liquid systems

We construct a generalized multiplicative renormalization group transformation to study the low energy dynamics of a heavy particle tunneling among $M$ different positions and interacting with $N_f$ independent conduction electron channels. Using a $1/N_f$-expansion we show that this M-level scales towards a fixed point equivalent to the $N_f$ channel $SU(M) \times SU(N_f)$ Coqblin-Schrieffer model. Solving numerically the scaling equations we find that a realistic M-level system scales close to this fixed point (FP) and its Kondo temperature is in the experimentally observable range $1-10 K$.Comment: 11 Latex pages, to appear in Phys. Rev. Lett, Figures available from the author by reques

Orbital Kondo behavior from dynamical structural defects

The interaction between an atom moving in a model double-well potential and the conduction electrons is treated using renormalization group methods in next-to-leading logarithmic order. A large number of excited states is taken into account and the Kondo temperature $T_K$ is computed as a function of barrier parameters. We find that for special parameters $T_K$ can be close to $1 {\rm K}$ and it can be of the same order of magnitude as the renormalized splitting $\Delta$. However, in the perturbative regime we always find that T_K \alt \Delta with a T_K \alt 1 {\rm K} [Aleiner {\em et al.}, Phys. Rev. Lett. {\bf 86}, 2629 (2001)]. We also find that $\Delta$ remains unrenormalized at energies above the Debye frequency, $\omega_{\rm Debye}$.Comment: 9 pages, 9 figures, RevTe

SU(4) Fermi Liquid State and Spin Filtering in a Double Quantum Dot System

We study a symmetrical double quantum dot (DD) system with strong capacitive inter-dot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift $\pi/4$. Application of an external magnetic field gives rise to a large magneto-conductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four lead setup we find perfectly spin polarized transmission.Comment: 4 pages, 4 figures, ReVTe

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

We investigate the charge fluctuations of a grain (large dot) coupled to a lead via a small quantum dot in the Kondo regime. We show that the strong entanglement of charge and spin flips in this setup can result in a stable SU(4) Kondo fixed point, which considerably smears out the Coulomb staircase behavior already in the weak tunneling limit. This behavior is robust enough to be experimentally observable.Comment: 4 pages, 1 figure, final version for PRB Rapid Com

Non-equilibrium transport theory of the singlet-triplet transition: perturbative approach

We use a simple iterative perturbation theory to study the singlet-triplet (ST) transition in lateral and vertical quantum dots, modeled by the non-equilibrium two-level Anderson model. To a great surprise, the region of stable perturbation theory extends to relatively strong interactions, and this simple approach is able to reproduce all experimentally-observed features of the ST transition, including the formation of a dip in the differential conductance of a lateral dot indicative of the two-stage Kondo effect, or the maximum in the linear conductance around the transition point. Choosing the right starting point to the perturbation theory is, however, crucial to obtain reliable and meaningful results

Kondo temperature of SU(4) symmetric quantum dots

A path integral approach is used to derive a closed analytical expression for the Kondo temperature of the SU(4) symmetrical Anderson model. In contrast to the SU(2) case, the prefactor of the Kondo temperature is found to display a peculiar orbital-energy (gate voltage) dependence, reflecting the presence of various SU(4) mixed valence fixed points. Our analytical expressions are tested against and confirmed by numerical renormalization group computations

Quantum Noise Measurement of a Carbon Nanotube Quantum Dot in the Kondo Regime

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $\nu$ of the order or higher than the frequency associated with the Kondo effect $k_B T_K/h$, with $T_K$ the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for $h \nu \approx k_B T_K$ a Kondo effect related singularity at a voltage bias $eV \approx h \nu$, and a strong reduction of this singularity for $h \nu \approx 3 k_B T_K$, in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the non-equilibrium dynamics of many-body phenomena in nanoscale devices.Comment: 6 pages, 4 figure