We develop a theoretical framework to study the influences of coupling asymmetry on the thermoelectrics of a strongly coupled SU($N$) Kondo impurity based on a local Fermi liquid theory. Applying non-equilibrium Keldysh formalism, we investigate charge current driven by the voltage bias and temperature gradient in the strong coupling regime of an asymmetrically coupled SU($N$) quantum impurity. The thermoelectric characterizations are made via non-linear Seebeck effects. We demonstrate that the beyond particle-hole (PH) symmetric SU($N$) Kondo variants are highly desirable with respect to the corresponding PH symmetric setups in order to have significantly improved thermoelectric performance. The greatly enhanced Seebeck coefficients by tailoring the coupling asymmetry of beyond PH symmetric SU($N$) Kondo effects are explored. Apart from presenting the analytical expressions of asymmetry dependent transport coefficients for general SU($N$) Kondo effects, we make a close connection of our findings with the experimentally studied SU(2) and SU(4) Kondo effects in quantum dot nano structures. Seebeck effects associated with the theoretically proposed SU(3) Kondo effects are discussed in detail.
We theoretically investigate the thermoelectric and spin thermoelectric properties of a T-shaped double quantum dot strongly coupled to two ferromagnetic leads, focusing on transport regime where the system exhibits the two-stage Kondo effect. We study the dependence of the (spin) Seebeck coefficient, the corresponding power factor and the figure of merit on temperature, leads' spin polarization and dot level position. We show that the thermal conductance fulfills a modified Wiedemann-Franz law. We also demonstrate that the spin thermopower is enhanced at temperatures corresponding to the seco…
We report on the first measurement of the Seebeck coefficient in a tunnel-contacted and gate-tunable individual single-quantum dot junction in the Kondo regime, fabricated using the electromigration technique. This fundamental thermoelectric parameter is obtained by directly monitoring the magnitude of the voltage induced in response to a temperature difference across the junction, while keeping a zero net tunneling current through the device. In contrast to bulk materials and single molecules probed in a scanning tunneling microscopy (STM) configuration, investigating the thermopower in nanos…
We study the multi-channel Kondo impurity dynamics realized in a mesoscopic superconducting island connected to metallic leads. The effective 'impurity spin' is non-locally realized by Majorana bound states and strongly coupled to lead electrons by non-Fermi liquid correlations. We explore the spin dynamics and its observable ramifications near the low-temperature fixed point. The topological protection of the system raises the perspective to observe multi-channel Kondo impurity dynamics in experimentally realistic environments.
We investigate electron transport under the two impurity Kondo problem with the Aharonov--Bohm and Aharonov--Casher effects. These interference effects induce the Ising-coupled Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction. We discuss the inter- and intra-site spin conductance as well as charge conductance in the Kondo and the mixed-valence regimes using the slave boson mean field approximation.
We theoretically study the nonequilibrium thermoelectric transport properties of a strongly-correlated molecule (or quantum dot) embedded in a tunnel junction. Assuming that the coupling of the molecule to the contacts is asymmetric, we determine the nonlinear current driven by the voltage and temperature gradients by using the perturbation theory. However, the subsystem consisting of the molecule strongly coupled to one of the contacts is solved by using the numerical renormalization group method, which allows for accurate description of Kondo correlations. We study the temperature gradient a…
We study the fate of the Kondo effect with one-dimensional conduction baths at very low densities, such that the system explores the bottom of the conduction band. This can involve either finite low densities, or a small number of fixed conduction electrons in a large system, i.e., the limit of large bath sizes can be taken with either fixed small density or with fixed number. We characterize the Kondo physics for such systems through the energy gain due to Kondo coupling, which is a general analog of the Kondo temperature scale, and through real-space profiles of densities and spin-spin corre…
We propose a method to directly measure, by electrical means, the Kondo screening cloud formed by an Anderson impurity coupled to semi-infinite quantum wires, on which an electrostatic gate voltage is applied at distance L from the impurity. We show that the Kondo cloud, and hence the Kondo temperature and the electron conductance through the impurity, are affected by the gate voltage, as L decreases below the Kondo cloud length. Based on this behavior, the cloud length can be experimentally identified by changing L with a keyboard type of gate voltage or tuning the coupling strength between t…
When a single magnetic adatom is deposited on a surface of a metal, it affects the charge and spin texture of the electron gas surrounding it. The screening of the local moment by conduction electrons gives rise to the Kondo effect. Here we investigate the effect of the Rashba spin orbit coupling on the local magnetization density of states (LMDOS) around a Cobalt impurity on a Au(111) surface in a magnetic field. We show that the in-plane component of the LMDOS is exclusively associated with the Rashba spin orbit interaction. This observation can be experimentally exploited to confirm the pre…
Using a simplified microscopic model of coupled spin and lattice excitations in a ferromagnetic insulator we evaluate the magnetic-field dependence of the spin Seebeck effect at low temperatures. The model includes Heisenberg exchange coupling, a harmonic lattice potential, and a pseudo-dipolar exchange interaction. Our approach goes beyond previous work [Phys. Rev. B 98, 134421 (2018)] in that it does not rely on the a priori assumption of a fast equilibration of the magnon and phonon distributions. Our theory shows that singular features in the magnetic-field dependence of the spin Seebeck e…
Quantum critical behavior in the two-impurity Kondo model requires the distinct separation of two scales, T_K >> T*, where T_K is the Kondo temperature and T* is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi liquid fixed point. We provide a derivation of T* based on the renormalization group to lowest order. This result is confirmed by a numerical renormalization group (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi liquid fixed point is derived and subsequently…
The Peltier effect is the reverse phenomenon of the Seebeck effect, and has been observed experimentally in nanoscale junctions. However, despite its promising applications in local cooling of nanoelectronic devices, the role of strong electron correlations on such a phenomenon is still unclear. Here, by analyzing the thermoelectric properties of quantum impurity systems out of equilibrium, we unveil the essential role of electron-electron interactions and quantum resonant states in Peltier cooling, leading to the prediction of the Kondo cooling phenomenon. The existence of such Kondo cooling …
We analyze the consequences of a first-order (in the effective Kondo coupling) inter-impurity correlation present in the Two-Impurity Anderson Hamiltonian. This correlation generates a pair of Kondo Doublet states which are responsible for the first (higher energy) Kondo stage of these systems. Applied to systems of quantum dots in a semiconductor heterolayer, these Doublets predict a mainly ferromagnetic dot-dot spin correlation which is different than the expected from the second-order RKKY interaction. In order to effectively screen both dots, a parallel alignment of the dot-spins is favore…
We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the cor…
We reobtain the Kondo-Doublet interaction by means of the Brillouin-Wigner Perturbation theory. By applying the same method to the single impurity case we show that the Kondo-Doublet interaction is a direct consequence of the Kondo screening cloud. We fully confirm our previous results on this novel interaction. In particular, we found that for values of the system parameters typical of semiconductor Quantum Dots heterostructures, the ferromagnetic Kondo-Doublet interaction dominates over the RKKY one.
We investigate thermoelectric transport through a SU(N) quantum impurity in the Kondo regime. The strong coupling fixed point theory is described by the local Fermi-liquid paradigm. Using Keldysh technique we analyse the electric current through the quantum impurity at both finite bias voltage and finite temperature drop across it. The theory of a steady state at zero-current provides a complete description of the Seebeck effect. We find pronounced non-linear effects in temperature drop at low temperatures. We illustrate the significance of the non-linearities for enhancement of thermopower by…
A system of two exchange-coupled Kondo impurities in a magnetic field gives rise to a rich phase space hosting a multitude of correlated phenomena. Magnetic atoms on surfaces probed through scanning tunnelling microscopy provide an excellent platform to investigate coupled impurities, but typical high Kondo temperatures prevent field-dependent studies from being performed, rendering large parts of the phase space inaccessible. We present an integral study of pairs of Co atoms on insulating Cu2N/Cu(100), which each have a Kondo temperature of only 2.6 K. In order to cover the different regions …
In order to quantify quantum entanglement in two impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the im…
We have carried out a generalized Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the low-energy spin interactions of the system. The second-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At fouth-order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling and a correlated Kondo coupling between the two impurities.
We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $\propto 1/ [ | ω\ | \ln ^{2}( Λ/| ω\ | \ ) \ ] $ near the Dirac point $ω\rightarrow …
We study the Kondo effect generated by a single magnetic impurity embedded in an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature, in a way that depends on the parity of the number of electrons on the grain. We show that the single-electron tunneling conductance through such a grain features Kondo-induced Fano-type resonances of measurable size, with an anomalous dependence on temperature and level spacing.
The combined effect of Rashba and Dresselhaus spin-orbit interactions on the physics of a helical Luttinger liquid coupled to a Kondo impurity is studied. A Rashba coupling can potentially destroy the Kondo singlet formation in certain parameter regimes [Phys. Rev. B 86, 161103(R) (2012)]. This effect is here shown to vanish for sufficiently strong Dresselhaus interaction. The transport properties of the system are investigated by calculating electrical conductance, current and current fluctuations, and thermal conductance.
We present a theoretical study based on the Anderson model of the transport properties of a Kondo impurity (atom or quantum dot) connected to ferromagnetic leads, which can sustain a non-equilibrium spin current. We analyze the case where the spin current is injected by an external source and when it is generated by the voltage bias. Due to the presence of ferromagnetic contacts, a static exchange field is produced that eventually destroys the Kondo correlations. We find that such a field can be compensated by an appropriated combination of the spin-dependent chemical potentials leading to the…
Nanoscale physics and dynamical mean field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single quantum impurity problems onto spin-chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic Kondo problem''. To study universal Kondo physics, a large ratio between the effective bandwidt…
In the strong coupling limit, an effective resonant level model is derived for the spin-1 underscreened Kondo impurity model. A local quantum critical behavior is induced by the formation of a bound state with partially screened magnetic moment, displaying a residual $Z_2$ symmetry, leading to a $δ$-resonance at the Fermi level in the impurity spectral function. As a consequence, a logarithmic singularity appears in the real part of the impurity dynamic spin susceptibility as a function of $\max (ω, T)$, with $ω$ as frequency, $T$ temperature. A small magnetic field breaks this $Z_2$ symmetry …
We study a series-coupled double quantum dot in the Kondo regime modeled by the two-impurity Anderson model and find a new conduction-band mediated superexchange interaction that competes with Kondo physics in the strong Coulomb interaction limit. Our numerical renormalization group results, complemented with the higher-order Rayleigh-Schrödinger perturbation theory, show that the novel exchange mechanism leads to clear experimental consequences that can be checked in transport measurements through double quantum dots.
The electronic properties of a Kondo impurity are investigated in a magnetic field using linear response theory. The distribution of electrical charge and magnetic polarization are calculated in real space. The (small) magnetic field does not change the charge distribution. However, it unmasks the Kondo cloud. The (equal) weight of the d-electron components with their magnetic moment up and down is shifted and the compensating s-electron clouds don't cancel any longer (a requirement for an experimental detection of the Kondo cloud). In addition to the net magnetic polarization of the conductio…
We analyze the effects of high energy configurations on the Kondo-doublet interaction between two Anderson impurities. We found that the Kondo doublet states are robust and that their coherence energy is incremented by the inclusion of high energy configurations. Analytic expressions are obtained for the corrections near the Kondo limit. Analysis of the system in the intermediate valence regime shows that the behavior of the system can be changed from ferromagnetic to sligthy antiferromagnetic by tuning the system parameters; this regime can also be used to study the interplay between hole-dri…
Although the Kondo effect and the Kondo ground state of a magnetic impurity have been investigated for more than forty years it was until recently difficult if not impossible to calculate spatial properties of the ground state. In particular the calculation of the spatial distribution of the so-called Kondo cloud or even its existence have been elusive. In recent years a new method has been introduced to investigate the properties of magnetic impurities, the FAIR method, where the abbreviation stands for Friedel Artificially Inserted Resonance. The FAIR solution of the Friedel-Anderson and the…
We consider a Kondo-like impurity interacting with fermions on a honeycomb lattice at half-filling, as in the case of graphene. We derive from the lattice model an effective one-dimensional continuum theory which has, in general, four flavors with angular momentum mixing in the presence of internode scattering processes and six couplings in the spin-isotropic case. Under particular conditions, however, it can be reduced to a single-coupling multichannel pseudogap Kondo model. We finally calculate, in the presence of an energy dependent Fermi velocity, induced by Coulomb interaction, the critic…
We investigate the time-dependent transport properties of single and double quantum-impurity systems based on the hierarchical equations of motion (HEOM) approach. In the Kondo regime, the dynamical current in both cases is found oscillating due to the temporal coherence of electrons tunneling through the device, which shares the same mechanism as the single-level resonance without e-e interactions but shows some different characteristics. For single quantum-impurity systems, the temperature T plays an inhibitory action to the oscillations of dynamic current through its suppression to the Kond…
We investigate theoretically the thermoelectric transport properties of a T-shaped double quantum dot side-coupled to a topological superconducting nanowire hosting Majorana zero-energy modes. The calculations are performed using the numerical renormalization group method focusing on the transport regime, where the system exhibits the two-stage Kondo effect. It is shown that the leakage of Majorana quasiparticles into the double dot system results in a half-suppression of the second stage of the Kondo effect, which is revealed through fractional values of the charge and heat conductances and g…
Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction - essential for having a well-controllable two-qubit gate - is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the pr…
We propose a model describing Seebeck effect on a weak link between two quantum systems with fine-tunable ground states of Fermi and Non-Fermi liquid origin. The experimental realization of the model can be achieved by utilizing the quantum devices operating in the Integer Quantum Hall regime [Z. Iftikhar et al, Nature 526, 233 (2015)] designed for detection of macroscopic quantum charged states in multi-channel Kondo systems. We present a theory of thermo-electric transport through hybrid quantum devices constructed from quantum dot - quantum point contact building blocks. We discuss pronounc…
We study the spatial distribution of the Kondo screening cloud. We find that in 3 D the spatial range of the cloud is limited to distances of the order of the Fermi wavelength due to angular dispersion effects. In lower dimensions this effect is less important and thus the Kondo length determines the localization of the cloud around the magnetic impurity. We clarify the role of the Kondo cloud in the impurity-impurity interactions: the hole coherence factor of the Kondo-doublet interaction is proportional to the amplitude of the Kondo cloud. We single out an experimental setup in which the Kon…
Tunneling conductance through two quantum dots, which are connected in series to left and right leads, is calculated by using the numerical renormalization group method. As the hopping between the dots increases from very small value, the following states continuously appear; (i) Kondo singlet state of each dot with its adjacent-site lead, (ii) singlet state between the local spins on the dots, and (iii) double occupancy in the bonding orbital of the two dots. The conductance shows peaks at the transition regions between these states. Especially, the peak at the boundary between (i) and (ii) h…
We study the ground-state entanglement properties of nanostructured Kondo systems consisting of a pair of impurity spins coupled to a background of confined electrons. The competition between the RKKY-like coupling and the Kondo effect determines the development of quantum correlations between the different parts of the system. A key element is the electronic filling due to confinement. An even electronic filling leads to results similar to those found previously for extended systems, where the properties of the reduced impurity-spin subsystem are uniquely determined by the spin correlation fu…
We investigate the many-body effects of a magnetic adatom in ferromagnetic graphene by using the numerical renormalization group method. The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials. For a half-filled impurity in undoped graphene, the presence of ferromagnetism can bring forth Kondo correlations, yielding two kink structures in the local spectral function near the Fermi energy. When the spin splitting of local occupations is compensated by an external magnetic field, the two Kondo ki…
Recent studies of mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to the potential realization of topological superconductivity. The Kondo exchange coupling J_K of such atoms with the electrons in the superconductor has a pair-breaking effect which produces so-called Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap, whose energetic positions are intimately connected with the requirements for topological superconductivity. Here, using the tip of a scanning tunneling microscope, we artificially craft a multi-impurity Kondo syst…
The screening of an impurity spin by conduction electrons is associated with the formation of a large Kondo screening cloud, of size xi_K. We study the quantum entanglement between a region of size r surrounding the impurity and the rest of the sample, (of total size R) using Density Matrix Renormalization Group and analytic methods. The corresponding "impurity entanglement entropy", S_{imp}, is shown to be a universal scaling function of r/xi_K and r/R. We calculate this universal function using Fermi liquid theory in the regime xi_K << r.
The Kondo effect, one of the oldest correlation phenomena known in condensed matter physics, has regained attention due to scanning tunneling spectroscopy (STS) experiments performed on single magnetic impurities. Despite the sub-nanometer resolution capability of local probe techniques one of the fundamental aspects of Kondo physics, its spatial extension, is still subject to discussion. Up to now all STS studies on single adsorbed atoms have shown that observable Kondo features rapidly vanish with increasing distance from the impurity. Here we report on a hitherto unobserved long range Kondo…
We investigate the nonequilibrum transport properties of a quantum dot when spin flip processes compete with the formation of a Kondo resonance in the presence of ferromagnetic leads. Based upon the Anderson Hamiltonian in the strongly interacting limit, we predict a splitting of the differential conductance when the spin flip scattering amplitude is of the order of the Kondo temperature. We discuss how the relative orientation of the lead magnetizations strongly influences the electronic current and the shot noise in a nontrivial way. Furthermore, we find that the zero-bias tunneling magnetor…
The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on t…
We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.
The archetypal two-impurity Kondo problem in a serially-coupled double quantum dot is investigated in the presence of a thermal bias $θ$. The slave-boson formulation is employed to obtain the nonlinear thermal and thermoelectrical responses. When the Kondo correlations prevail over the antiferromagnetic coupling $J$ between dot spins we demonstrate that the setup shows negative differential thermal conductance regions behaving as a thermal diode. Besides, we report a sign reversal of the thermoelectric current $I(θ)$ controlled by $t/Γ$ ($t$ and $Γ$ denote the interdot tunnel and reservoir-dot…
We theoretically analyze a state-of-the-art experimental method based on a combination of electron spin resonance and scanning tunneling microscopy (ESR-STM), to directly probe the spin fluctuations in the Kondo effect. The Kondo impurity is exchange coupled to the probe spin, and the ESR-STM setup detects the small level shifts in the probe spin induced by the spin fluctuations of the Kondo impurity. We use the open quantum system approach by regarding the probe spin as the "system" and the Kondo impurity spin as the fluctuating "bath" to evaluate the resonance line shifts in terms of the dyn…
We consider a magnetic s=1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain $J_1$ and the coupling between the two sites $J_2$. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a non-trivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-…
We analyze the two Anderson impurity problem, in the strong Coulomb repulsion limit, by means of variational wave functions whose equations we solve analytically. We found two pairs of Doublet states, one odd and one even with respect to the midplane between the impurities. These Doublets make a significatively strong use of the hybridization terms of the Hamiltonian, and have a much larger Kondo-like correlation energy than a single impurity (the Kondo energy). Furthermore, these Doublets combine to form a Super-Singlet. This Super-Singlet makes use of the remaining hybridization probability …
We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting `Kondo polaron' takes the universal form $μ\to \frac{3\hbar v_F^2}{2πk_B^2T^2}$, in sharp contrast to the spinless case where …
We consider a quantum dot with ${\cal K}{\geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fe…
Quantum entanglement between an impurity and its environment is expected to be central in quantum impurity problems. We develop a method to compute the entanglement in spin-1/2 impurity problems, based on the entanglement negativity and the boundary conformal field theory (BCFT). Using the method, we study the thermal decay of the entanglement in the multichannel Kondo effects. At zero temperature, the entanglement has the maximal value independent of the number of the screening channels. At low temperature, the entanglement exhibits a power-law thermal decay. The power-law exponent equals two…
It is well established that a correlated quantum impurity embedded in a metallic host can form the many-body Kondo state with itinerant electrons due to the effective antiferromagnetic coupling. Such effect is manifested spectroscopically by a narrow Abrikosov-Suhl peak appearing at the Fermi level below a characteristic temperature T_K. Recent experiments using nanoscopic heterojunctions where the correlated quantum impurities (dots) are coupled to superconducting reservoirs revealed that the Kondo-type correlations are substantially weaker because: i) the single-particle states of supercondu…
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 $Δ= dI/dV$ observed in the quantum mirage experiment is reproduced. In presence of another impurity, $Δ= dI/dV$ 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 resonanc…
We study the nonequilibrium dynamics of a periodically-driven anisotropic Kondo impurity model. The periodic time dependence is introduced for a local magnetic field which couples to the impurity spin and also for an in-plane exchange interaction. We obtain the exact results on the time evolution for arbitrary periodic time dependence at the special point in the parameter space known as the Toulouse limit. We first consider a specific case where the local magnetic field is periodically switched on and off. When the driving period is much shorter than the inverse of the Kondo temperature, an in…
