Many-body theory of the quantum mirage

In recent scanning tunneling microscopy experiments, confinement in an elliptical corral has been used to project the Kondo effect from one focus to the other one. I solve the Anderson model at arbitrary temperatures, for an impurity hybridized with eigenstates of an elliptical corral, each of which has a resonant level width delta. This width is crucial. If delta < 20 meV, the Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For particular conditions, a stronger mirage with the impurity out of the foci is predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a reference included to show that the hybridization of the impurity with bulk states can be neglecte

Quantum Interference between Impurities: Creating Novel Many-Body States in s-wave Superconductors

We demonstrate that quantum interference of electronic waves that are scattered by multiple magnetic impurities in an s-wave superconductor gives rise to novel bound states. We predict that by varying the inter-impurity distance or the relative angle between the impurity spins, the states' quantum numbers, as well as their distinct frequency and spatial dependencies, can be altered. Finally, we show that the superconductor can be driven through multiple local crossovers in which its spin polarization, $$, changes between $=0, 1/2$ and 1.Comment: 4 pages, 4 figure

Interaction between Kondo impurities in a quantum corral

We calculate the spectral densities for two impurities inside an elliptical quantum corral using exact diagonalization in the relevant Hilbert subspace and embedding into the rest of the system. For one impurity, the space and energy dependence of the change in differential conductance $\Delta = dI/dV$ observed in the quantum mirage experiment is reproduced. In presence of another impurity, $\Delta = dI/dV$ is very sensitive to the hybridization between impurity and bulk. The impurities are correlated ferromagnetically between them. A hopping $\gtrsim 0.15$ eV between impurities destroy the Kondo resonance.Comment: 4 pages, 4 figure

Quantum interference between non-magnetic impurities in d_x2-y2-wave superconductors

We study quantum interference of electronic waves that are scattered by multiple non-magnetic impurities in a d_x2-y2-wave superconductor. We show that the number of resonance states in the density-of-states (DOS), as well as their frequency and spatial dependence change significantly as the distance between the impurities or their orientation relative to the crystal lattice is varied. Since the latter effect arises from the momentum dependence of the superconducting gap, we argue that quantum interference is a novel tool to identify the symmetry of unconventional superconductors.Comment: 4 pages, 4 figure

One- and many-body effects on mirages in quantum corrals

Recent interesting experiments used scanning tunneling microscopy to study systems involving Kondo impurities in quantum corrals assembled on Cu or noble metal surfaces. The solution of the two-dimensional one-particle Schrodinger equation in a hard wall corral without impurity is useful to predict the conditions under which the Kondo effect can be projected to a remote location (the quantum mirage). To model a soft circular corral, we solve this equation under the potential W*delta(r-r0), where r is the distance to the center of the corral and r0 its radius. We expand the Green's function of electron surface states Gs0 for r<r0 as a discrete sum of contributions from single poles at energies epsilon_i-I*delta_i. The imaginary part delta_i is the half-width of the resonance produced by the soft confining potential, and turns out to be a simple increasing function of epsilon_i. In presence of an impurity, we solve the Anderson model at arbitrary temperatures using the resulting expression for Gs0 and perturbation theory up to second order in the Coulomb repulsion U. We calculate the resulting change in the differential conductance Delta dI/dV as a function of voltage and space, in circular and elliptical corrals, for different conditions, including those corresponding to recent experiments. The main features are reproduced. The role of the direct hybridization between impurity and bulk, the confinement potential, the size of the corral and temperature on the intensity of the mirage are analyzed. We also calculate spin-spin correlation functions.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev. B. Calculations of spin correlations within an additional approximation adde

Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.Comment: 9 pages, 8 figure

Anomalous behavior of spin wave resonances in Ga_{1-x}Mn_{x}As thin films

We report ferromagnetic and spin wave resonance absorption measurements on high quality epitaxially grown Ga_{1-x}Mn_{x}As thin films. We find that these films exhibit robust ferromagnetic long-range order, based on the fact that up to seven resonances are detected at low temperatures, and the resonance structure survives to temperatures close to the ferromagnetic transition. On the other hand, we observe a spin wave dispersion which is linear in mode number, in qualitative contrast with the quadratic dispersion expected for homogeneous samples. We perform a detailed numerical analysis of the experimental data and provide analytical calculations to demonstrate that such a linear dispersion is incompatible with uniform magnetic parameters. Our theoretical analysis of the ferromagnetic resonance data, combined with the knowledge that strain-induced anisotropy is definitely present in these films, suggests that a spatially dependent magnetic anisotropy is the most likely reason behind the anomalous behavior observed.Comment: 9 pages, including 6 figure

Kondo effect in systems with dynamical symmetries

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets $|S_{i}M_{i}>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_{i}}$ are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators ${\bf R}_{n}$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $\ne 0$. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin ${\bf s}$ with the operators of the dot then contains new exchange terms, $J_{n} {\bf s} \cdot {\bf R}_{n}$ beside the ubiquitous ones $J_{i} {\bf s}\cdot {\bf S}_{i}$. The operators ${\bf S}_{i}$ and ${\bf R}_{n}$ generate a dynamical group (usually SO(n)). Remarkably, the value of $n$ can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators ${\bf R}_{n}$ and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in triple quantum dot with four electrons.Comment: 24 two-column page

Magnetic susceptibilities of diluted magnetic semiconductors and anomalous Hall-voltage noise

The carrier spin and impurity spin densities in diluted magnetic semiconductors are considered using a semiclassical approach. Equations of motions for the spin densities and the carrier spin current density in the paramagnetic phase are derived, exhibiting their coupled diffusive dynamics. The dynamical spin susceptibilities are obtained from these equations. The theory holds for p-type and n-type semiconductors doped with magnetic ions of arbitrary spin quantum number. Spin-orbit coupling in the valence band is shown to lead to anisotropic spin diffusion and to a suppression of the Curie temperature in p-type materials. As an application we derive the Hall-voltage noise in the paramagnetic phase. This quantity is critically enhanced close to the Curie temperature due to the contribution from the anomalous Hall effect.Comment: 18 pages, 1 figure include

Quantum Dot in the Kondo Regime coupled to p-wave superconductors

This paper studies the physics of junctions containing superconducting $(S)$ and normal $(N)$ leads weakly coupled to an Anderson impurity in the Kondo regime $(K)$. Special attention is devoted to the case where one of the leads is a $p-wave$ superconductor where mid-gap surface states play an important role in the tunneling processes and help the formation of Kondo resonance. The novel physics in these systems beyond that encountered in quantum dots coupled only to to normal leads is that electron transport at finite bias $eV$ in $SKN$ and $SKS$ junctions is governed by Andreev reflections. These enable the occurrence of dissipative current even when the bias $eV$ is smaller than the superconducting gap $\Delta$. Using the slave boson mean field approximation the current, shot-noise power and Fano factor are calculated as functions of the applied bias voltage in the sub-gap region $eV < \Delta$ and found to be strongly dependent on the ratio $t_K$ between the Kondo temperature $T_{K}$ and the superconducting gap $\Delta$. In particular, for large values of $t_K$ the attenuation of current due to the existence of the superconducting gap is compensated by the Kondo effect. This scenario is manifested also in the behavior of the Josephson current as function of temperature.Comment: 7 pages, 5 .eps figure