Kondo screening cloud and the charge staircase in one-dimensional mesoscopic devices
Rodrigo G. Pereira, Nicolas Laflorencie, Ian Affleck, Bertrand I. Halperin
备注：
This is an extended version of cond-mat/0612635 with an analysis of bulk Luttinger liquid interactions added as well as a discussion of experimental possibilities
We propose that the finite size of the Kondo screening cloud, xi_K, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential, mu in the system is varied at zero temperature, one should observe charge steps whose locations are at values of mu that are controlled by the Kondo effect when the system size L is comparable to xi_K. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of xi_K/L. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.
We develop a theoretical proposal for the charge Kondo effect in mesoscopic normal-superconductor-normal heterostructures, where the superconducting gap exceeds the electrostatic charging energy. Charge-Kondo correlations in these devices alter the conventional temperature-dependence of Andreev reflection and electron cotunneling. We predict typical Kondo temperatures of $\gtrsim 10 {\rm mK}$, and suggest experimental architectures that combine superconducting charge-qubits with semiconducting nanowires at cryogenic temperatures.
We study how finite size effects may appear when a quantum dot in the Kondo Coulomb blockade regime is embedded into a mesoscopic device with finite wires. These finite size effects appear when the size of the mesoscopic device containing the quantum dot is of the order of the size of Kondo cloud and affect all thermodynamic and transport properties of the Kondo quantum dot. We also generalize our results to the experimentally relevant case where the wires contain several transverse modes/channels. Our results are based on perturbation theory, Fermi liquid theory and slave boson mean field the…
We study the non-equilibrium noise in mesoscopic diffusive wires hosting magnetic impurities. We find that the shot-noise to current ratio develops a peak at intermediate source-drain biases of the order of the Kondo temperature. The enhanced impurity contribution at intermediate biases is also manifested in the effective distribution. The predicted peak represents increased inelastic scattering rate at the non-equilibrium Kondo crossover.
Phase-sensitive transport through a quantum dot coupled to an Aharonov-Bohm ring is analyzed. In this geometry the spectral density of states is directly related to the conductance. It is shown that the Kondo resonance depends on the phase and on the total number of electrons (modulo 4) in the mesoscopic ring. The effect of the discrete level spacing in the ring and of the coupling to the electrical leads is discussed.
The magnitude and phase of the transmission amplitude of a multi-level quantum dot is calculated for the mesoscopic regime of level spacing large compared to level width. The interplay between Kondo correlations and the influence by neighboring levels is discussed. As in the single-level case, the Kondo plateaus of magnitude and phase disappear with increasing temperature. At certain gate voltages, ``stationary'' points are found at which the transmission phase is independent of temperature. Depending on the mesoscopic parameters of the adjacent levels (like relative sign and magnitude of tunn…
We study the mesoscopic Kondo box, consisting of a quantum spin 1/2 interacting with a chaotic electronic bath as can be realized by a magnetic impurity coupled to electrons on a quantum dot, using a mean-field approach for the Kondo interaction. Its umerical efficiency allows us to analyze the Kondo temperature, the local magnetic susceptibility, and the conductance statistics for a large number of samples with energy levels obtained by random matrix theory. We see pronounced parity effects in the average values and in the probability distributions, depending on an even and odd electronic occ…
The persistent current through a quantum dot inserted in a mesoscopic ring of length L is studied. A cluster representing the dot and its vicinity is exactly diagonalized and embedded into the rest of the ring. The Kondo resonance provides a new channel for the current to flow. It is shown that due to scaling properties, the persistent current at the Kondo regime is enhanced relative to the current flowing either when the dot is at resonance or along a perfect ring of same length. In the Kondo regime the current scales as $L^{-1/2}$, unlike the $L^{-1}$ scaling of a perfect ring. We discuss th…
The tunneling conductances of a quantum point contact and a magnetized atom adsorbed on an insulating layer above a metallic substrate are obtained by considering the coherent transport of the entangled and nonentangled Kondo singlets, and these are compared with the experimental results. Spins of the entangled Kondo singlet flow unidirectionally in a sequential up-and-down manner. This transport does not follow linear response theory. The nonentangled Kondo singlet performs resonant tunneling through a coherent transport channel and yields coherent side peaks at a finite bias. The coherent tr…
We study the persistent current circulating along a mesoscopic ring with a dot side-coupled to it when threaded by a magnetic field. A cluster including the dot and its vicinity is diagonalized and embedded into the rest of the system. The result is numerically exact. We show that a ring of any size can be in the Kondo regime, although for small sizes it depends upon the magnetic flux. In the Kondo regime, the current can be a smooth or a strongly dependent function of the gate potential according to the structure of occupation of the highest energetic electrons of the system.
An interacting quantum dot inserted in a mesoscopic ring is investigated. A variational ansatz is employed to describe the ground state of the system in the presence of the Aharonov-Bohm flux. It is shown that, for even number of electrons with the energy level spacing smaller than the Kondo temperature, the persistent current has a value similar to that of a perfect ring with the same radius. On the other hand, for a ring with odd number electrons, the persistent current is found to be strongly suppressed compared to that of an ideal ring, which implies the suppression of the Kondo-resonant t…
We study the non-equilibrium regime of the Kondo effect in a quantum dot laterally coupled to a narrow wire. We observe a split Kondo resonance when a finite bias voltage is imposed across the wire. The splitting is attributed to the creation of a double-step Fermi distribution function in the wire. Kondo correlations are strongly suppressed when the voltage across the wire exceeds the Kondo temperature. A perpendicular magnetic field enables us to selectively control the coupling between the dot and the two Fermi seas in the wire. Already at fields of order 0.1 T only the Kondo resonance asso…
We study the Kondo effect of a quantum dot placed in a complex mesoscopic structure. Assuming that electronic interactions are taking place solely on the dot, and focusing on the infinite Hubbard interaction limit, we use a decoupling scheme to obtain an explicit analytic approximate expression for the dot Green function, which fulfills certain Fermi-liquid relations at zero temperature. The details of the complex structure enter into this expression only via the self-energy for the non-interacting case. The effectiveness of the expression is demonstrated for the single impurity Anderson model…
We report the observation of an anomalous magnetoresistance in extremely dilute quasi-one-dimensional AuFe wires at low temperatures, along with a hysteretic background at low fields. The Kondo resistivity does not show the unitarity limit down to the lowest temperature, implying uncompensated spin states. We suggest that the anomalous magnetoresistance may be understood as the interference correction from the accumulation of geometric phase in the conduction electron wave function around the localized impurity spin.
We study the Kondo effect in a quantum dot embedded in a mesoscopic ring taking into account intradot spin-flip scattering $R$. Based on the finite-$U$ slave-boson mean-field approach, we find that the Kondo peak in the density of states is split into two peaks by this coherent spin-flip transition, which is responsible for some interesting features of the Kondo-assisted persistent current circulating the ring: (1) strong suppression and crossover to a sine function form with increasing $R$; (2) appearance of a "hump" in the $R$-dependent behavior for odd parity. $R$-induced reverse of the per…
A dilute concentration of magnetic impurities can dramatically affect the transport properties of an otherwise pure metal. This phenomenon, known as the Kondo effect, originates from the interactions of individual magnetic impurities with the conduction electrons. Nearly a decade ago, the Kondo effect was observed in a new system, in which the magnetic moment stems from a single unpaired spin in a lithographically defined quantum dot, or artificial atom. The discovery of the Kondo effect in artificial atoms spurred a revival in the study of Kondo physics, due in part to the unprecedented contr…
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…
We present measurements of the magnetoconductance of long and narrow quasi one-dimensional gold wires containing magnetic iron impurities in a temperature range extending from $15 $mK to $4.2 $K. The dephasing rate extracted from the weak antilocalisation shows a pronounced plateau in a temperature region of $300 $mK - $800 $mK, associated with the phase breaking due to the Kondo effect. Below the Kondo temperature the dephasing rate decreases linearly with temperature, in contradiction with standard Fermi-liquid theory. Our data suggest that the formation of a spin glass due to the interactio…
The Kondo temperature of a magnetic impurity in a weakly disordered metal is distributed due to the randomness in the local exchange coupling, and the local electronic density of states (LDOS). We show that in a closed, phase coherent metal particle the resulting distribution of $T_K$ is strongly asymmetric and scales with the mean level spacing $Δ$. Its width is $2 \sqrt{Δ/βT_K}$, where $Δ$ is the mean level spacing, and $β=1,2$, with, without time reversal symmetry, respectively. Increasing the density of magnetic impurities, the distribution of Kondo temperatures (DKT) is found to become mo…
We propose that the finite size of the Kondo screening cloud, xi_K, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential in the system is varied at zero temperature, one should observe charge steps that are controlled by the Kondo effect when the system size L is comparable to xi_K. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of xi_K/L.
We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the `conditional evolution' of the Kondo singlet under projective measurement on the detector. O…
The temperature ($T$) - magnetic field ($H$) phase diagram for the tetragonal layered compound CeSbSe, is determined from magnetization, specific heat, and electrical resistivity measurements. This system exhibits complex magnetic ordering at $T_{\rm{M}}$ $=$ 3 K and the application of a magnetic field results in a cascade of magnetically ordered states for $H$ $\lesssim$ 1.8 T which are characterized by fractional integer size steps: i.e., a possible Devil's staircase is observed. Electrical transport measurements show a weak temperature dependence and large residual resistivity which suggest…
We present measurements of the magnetoresistance of long and narrow quasi one-dimensional gold wires containing magnetic iron impurities. The electron phase coherence time extracted from the weak antilocalisation shows a pronounced plateau in a temperature region of 300 mK - 800 mK, associated with the phase breaking due to the Kondo effect. Below the Kondo temperature, the phase coherence time increases, as expected in the framework of Kondo physics. At much lower temperatures, the phase coherence time saturates again, in contradiction with standard Fermi liquid theory. In the same temperatur…
Recently we have developed a theory of Keldysh formalism for mesoscopic systems. The resulting nonequilibrium Kubo formula for differential conductance makes it possible to propose the new formula of shot noise $S_h$, and thus to study shot noise in correlated systems at any temperature and any bias voltage. Employing this new approach, we analyze shot noise in the Kondo regime through a quantum dot for the symmetric case at zero temperature. Using the renormalized perturbation theory, we prove that in the leading order of bias voltage $S_h$ equal to noise power at zero temperature conventiona…
We study the finite size effect of the Kondo screening cloud in a double-quantum-dot setup via a large-N slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size $L$ and the other dot is side-coupled to the embedded dot via an anti-ferromagnetic spin-spin exchange coupling with the strength K. The antiferromagnetic coupling favors the local spin-singlet and suppresses the Kondo screening. The effective Kondo temperature T_k (proptotional to the inverse of the Kondo screening cloud size) shows the Kosterlitz--Thouless (KT) scaling at …
We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a side-branch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a current which, in the str…
We consider a Kondo spin that is coupled antiferromagnetically to a large chaotic quantum dot. Such a dot is described by the so-called universal Hamiltonian and its electrons are interacting via a ferromagnetic exchange interaction. We derive an effective Hamiltonian in the limit of strong Kondo coupling, where the screened Kondo spin effectively removes one electron from the dot. We find that the exchange coupling constant in this reduced dot (with one less electron) is renormalized and that new interaction terms appear beyond the conventional terms of the strong-coupling limit. The eigenene…
There are strong recent indications that the Kondo phenomena play important role in the electronic transport and dephasing mechanism for some of the experimentally investigated metallic samples. The spin and the orbital Kondo problem with two-level systems provide very similar behavior above the Kondo temperature. Below the Kondo temperature the behavior is drastically different as in the latter case the entropy remains non zero. In the following several results derived earlier by different methods are simply reproduced by the time-ordered diagram technique in the leading logarithmic approxima…
We study the Kondo screening effect generated by a single-electron transistor or quantum dot embedded in a small metallic ring. When the ring circumference $L$ becomes comparable to the fundamental length scale $ξ_K^0=\hbar \upsilon _F/T_K^0$ associated with the {\it bulk} Kondo tempe the Kondo resonance is strongly affected, depending on the total number of electrons ({\it modulo} 4) and magnetic flux threading the ring. The resulting Kondo-assisted persistent currents are also calculated in both Kondo and mixed valence regimes, and the maximum values are found in the crossover region.
We investigate theoretically the transport properties of a closed Aharonov-Bohm interferometer containing two quantum dots in the strong coupling regime. We find two distinct physical scenarios depending on the strength of the interdot Coulomb interaction. When the interdot Coulomb interaction is negligible only spin fluctuations are important and each dot develops a Kondo resonance at the Fermi level independently of the applied magnetic flux. The transport is characterized by the interference of these two independent Kondo resonances. On the contrary, for large interdot interaction, only one…
We investigate the persistent current influenced by the spin fluctuations in a mesoscopic ring weakly coupled to a quantum dot. It is shown that the Kondo effect gives rise to some unusual features of the persistent current in the limit where the charge transfer between two subsystems is suppressed. Various aspects of the crossover from a delocalized to a localized dot limit are discussed in relation with the effect of the coherent response of the Kondo cloud to the Aharonov-Bohm flux.
Following the discovery of the Kondo effect the bulk transport and magnetic behavior of the dilute magnetic alloys have been successfully described. In the last fifteen years new directions have been developed as the study of the systems of reduced dimensions and the artificial atoms so called quantum dots. In this review the first subject is reviewed starting with the scanning tunneling microscope (STM) study of a single magnetic impurity. The next subject is the reduction of the amplitude of the Kondo effect in samples of reduced dimension which was explained by the surface magnetic anisotro…
We study the local density of states (LDOS) in systems of Luttinger-liquid nanowires connected to a common mesoscopic superconducting island, in which Majorana bound states give rise to different types of topological Kondo effects. We show that electron interactions enhance the low-energy LDOS in the leads close to the island, with unusual exponents due to Kondo physics that can be probed in tunneling experiments.
We study a mesoscopic interacting quantum dot described by the "universal Hamiltonian" that is coupled to a Kondo spin. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground state spin; this Stoner staircase is modified non-trivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The problem is solved numerically by diagonalizing the system Hamiltonian in a customized good-spin basis and analytically in …
The Kondo effect may develop in those cases where there are non-commuting operators describing the interaction between the conduction electrons and impurities or defects with internal degrees of freedom. This interaction may involve spin or orbital variables. There are cases where the conduction electrons have conserved quantum numbers that do not appear in the coupling. An example is where the Kondo effect involves orbital degrees of freedom, and the interaction is independent of the real spins of the electrons, which are conserved and lead to the two-channel Kondo (2CK) problem. The low temp…
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.
This is a popular review of some recent investigations of the Kondo effect in a variety of mesoscopic systems. After a brief introduction, experiments are described where a scanning tunneling microscope measures the surroundings of a magnetic impurity on a metal surface. In another set of experiments, Kondo effect creates a number of characteristic features in the electron transport through small electronic devices -- semiconductor quantum dots or single-molecule transistors which can be tuned by applying appropriate gate voltages. The article contains 5 color figures, photo of Jun Kondo, but …
The current noise through a mesoscopic quantum dot is calculated and analyzed in the Fermi liquid regime of the SU(N) Kondo model. Results connect the Johnson-Nyquist noise to the shot noise for an arbitrary ratio of voltage and temperature, and show that temperature corrections are sizeable in usual experiments. For the experimentally relevant SU(4) case, quasiparticle interactions are shown to increase the shot noise.
The role of discrete orbital symmetry in mesoscopic physics is manifested in a system consisting of three identical quantum dots forming an equilateral triangle. Under a perpendicular magnetic field, this system demonstrates a unique combination of Kondo and Aharonov-Bohm features due to an interplay between continuous [spin-rotation SU(2)] and discrete (permutation C3v) symmetries, as well as U(1) gauge invariance. The conductance as a function of magnetic flux displays sharp enhancement or complete suppression depending on contact setups.
The coherence and phase evolution of electrons in a mesoscopic system in the Kondo correlated regime were studied. The Kondo effect, in turn, is one of the most fundamental many-body effects where a localized spin interacts with conduction electrons in a conductor. Results were obtained by embedding a quantum dot (QD) in a double path electronic interferometer and measuring interference of electron waves. The Phase was found to evolve in a range twice as large as the theoretically predicted one. Moreover, the phase proved to be highly sensitive to the onset of Kondo correlation, thus serving a…
We investigate a mesoscopic setup composed of a small electron droplet (dot) coupled to a larger quantum dot (grain) also subject to Coulomb blockade as well as two macroscopic leads used as source and drain. An exotic Kondo ground state other than the standard SU(2) Fermi liquid unambiguously emerges: an SU(4) Kondo correlated liquid. The transport properties through the small dot are analyzed for this regime, through boundary conformal field theory, and allow a clear distinction with other regimes such as a two-channel spin state or a two-channel orbital state.
We consider electromechanical properties of a single-electronic device consisting of movable quantum dot attached to a vibrating cantilever, forming a tunnel contact with a non-movable source electrode. We show that the resonance Kondo tunneling of electrons amplify exponentially the strength of nanoelectromechanical (NEM) coupling in such device and makes the latter to be insensitive to mesoscopic fluctuations of electronic levels in a nano-dot. It is also shown that the study of Kondo-NEM phenomenon provides an additional (as compared with a standard conductance measurements in a non-mechani…
We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe…
The Kondo effect is a striking consequence of the coupling of itinerant electrons to a quantum spin with degenerate energy levels. While degeneracies are commonly thought to arise from symmetries or fine-tuning of parameters, the recent emergence of Majorana fermions has brought to the fore an entirely different possibility: a "topological degeneracy" which arises from the nonlocal character of Majorana fermions. Here we show that nonlocal quantum spins formed from these degrees of freedom give rise to a novel "topological Kondo effect". This leads to a robust non-Fermi liquid behavior, known …
An Aharonov-Bohm interferometer (ABI) carrying a quantum dot on one of its arms is analyzed. It is found that the Kondo temperature of the device depends strongly on the magnetic flux penetrating the ring. As a result, mesoscopic finite-size effects appear when the Kondo temperature of the dot on the ABI is significantly smaller than the nominal one of the quantum dot (when not on the interferometer), leading to plateaus in the finite-temperature conductance as function of the flux. The possibility to deduce the transmission phase shift of the quantum dot from measurements of the ABI conductan…
Using the Anderson model in the Kondo regime, we calculate the persistent current j in a ring with an embedded quantum dot (QD) as a function of the Aharonov-Bohm flux Phi for different ring length L, temperature T and broadening of the conduction states delta . For T=delta =0 and L >> xi, where xi is the Kondo screening length, Lj tends to the value for a non interacting ideal ring, while it is suppressed for a side coupled QD. For any L/xi, Lj is also suppressed when either T or delta increase above a fraction of the level spacing which depends on Phi.
The transport in mesoscopic wires with large applied bias voltage has recently attracted great interest by measuring the energy distribution of the electrons at a given point of the wire, in Saclay. In the diffusive limit with negligible energy relaxation that shows two sharp steps at the Fermi energies of the two contacts, which are broadened due to the energy relaxation. In some of the experiments the broadening is reflecting an anomalous energy relaxation rate proportional to $E^{-2}$ instead of $E^{-3/2}$ valid for Coulomb electron-electron interaction, where $E$ is the energy transfer. La…
We investigate the charge fluctuations of a single-electron box (metallic grain) coupled to a lead via a smaller quantum dot in the Kondo regime. The most interesting aspect of this problem resides in the interplay between spin Kondo physics stemming from the screening of the spin of the small dot and orbital Kondo physics emerging when charging states of the grain with (charge) Q=0 and Q=e are almost degenerate. Combining Wilson's numerical renormalization-group method with perturbative scaling approaches we push forward our previous work [K. Le Hur and P. Simon, Phys. Rev. B 67, 201308R (200…
We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $ν=2+k/(k+2)$ or its particle-hole conjugate at $ν=2+2/(k+2)$. The $k$-channel Kondo model is channel isotropic even without fine tuning in the former state; in the latter, it is generically channel anisotropic. …
The charging of a quantum box connected to a lead by a single-mode point contact is solved for arbitrary temperatures, tunneling amplitudes, and gate voltages, using a variant of Wilson's numerical renormalization group. The charge inside the box and the capacitance of the junction are calculated on equal footing for all physical regimes, including weak tunneling, near perfect transmission, and the crossover regime in between. At the charge plateaus, perturbation theory is found to break down at fairly small tunneling amplitudes. Near perfect transmission, we confirm Matveev's scenario for the…
We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (θ) deformation of the ladder and interpolates between the isotropic ladder (θ=0) and the SU(2) ferromagnetic Kondo necklace model (θ=π). We show that the ground state in the (θ,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from Δ/…
The topological Kondo effect arises when conduction electrons in metallic leads are coupled to a mesoscopic superconducting island with Majorana fermions. Working with its minimal setup, we study the lead electron local tunneling density of states in its thermally smeared form motivated by scanning tunneling microscopy, focusing on the component $ρ_{2 k_F}$ oscillating at twice the Fermi wavenumber. As a function of temperature $T$ and at zero bias, we find that the amplitude of $ρ_{2 k_F}$ is nonmonotonic, whereby with decreasing $T$ an exponential thermal-length-controlled increase, potentia…
A fundamental prediction of scaling theories of the Kondo effect is the screening of an impurity spin by a cloud of electrons spread out over a mesoscopic distance. This cloud has never been observed experimentally. Recently, aspects of the Kondo effect have been observed in experiments on quantum dots embedded in quantum wires. Since the length of the wire may be of order the size of the screening cloud, such systems provide an ideal opportunity to observe it. We point out that persistent current measurements in a closed ring provide a conceptually simple way of detecting this fundamental len…
Conduction electrons coupled to a mesoscopic superconducting island hosting Majorana bound states have been shown to display a topological Kondo effect with robust non-Fermi liquid correlations. With $M$ bound states coupled to $M$ leads, this is an SO($M$) Kondo problem, with the asymptotic high and low energy theories known from bosonization and conformal field theory studies. Here we complement these approaches by analyzing the Bethe ansatz equations describing the exact solution of these models at all energy scales. We apply our findings to obtain nonperturbative results on the thermodynam…
We investigate theoretically quantum transport through the "charge" Kondo circuit consisting of the quantum dot (QD) coupled weakly to an electrode at temperature $T+ΔT$ and connected strongly to another electrode at the reference temperature $T$ by a single-mode quantum point contact (QPC). To account for the effects of Coulomb interaction in the QD-QPC setup operating in the integer quantum Hall regime we describe the edge current in the quantum circuit by Luttinger model characterized by the Luttinger parameter $g$. It is shown that the temperature dependence of both electric conductance $G…
We study the interplay between Coulomb blockade and the Kondo effect in quantum dots. We use a self-consistent scheme which describes mesoscopic devices in terms of a collective phase variable (slave rotor) and quasiparticle degrees of freedom. In the strong Coulomb blockade regime, we recover the description of metallic islands in terms of a phase only action. For a dot with well-separated levels, our method leads to the Kondo effect. We identify the regime where a crossover between the Coulomb blockade regime at high temperatures and the formation of a Kondo resonance at lower temperature ta…
We analyze the Kondo effect of a magnetic impurity attached to an ultrasmall metallic wire using the density matrix renormalization group. The spatial spin correlation function and the impurity spectral density are computed for system sizes of up to L=511 sites, covering the crossover from $L<\ell_K$ to $L > \ell_K$, with $\ell_K$ the spin screening length. %Strong mesoscopic variations of the Kondo temperature $T_K$ %and of the spectral features override, to some extent, the %even/odd effect predicted earlier for averaged quantities. We establish a proportionality between the weight of the Ko…
The magnetic properties of a system of coexisting localized spins and conduction electrons are investigated within an extended version of the one dimensional Kondo lattice model in which effects stemming from the electron-lattice and on-site Coulomb interactions are explicitly included. After bosonizing the conduction electrons, is it observed that intrinsic inhomogeneities with the statistical scaling properties of a Griffiths phase appear, and determine the spin structure of the localized impurities. The appearance of the inhomogeneities is enhanced by appropriate phonons and acts destructiv…
The magnetic properties of a system of coexisting localized spins and conduction electrons are investigated within an extended version of the one dimensional Kondo lattice model in which effects stemming from the electron-lattice and on-site Coulomb interactions are explicitly included. After bosonizing the conduction electrons, is it observed that intrinsic inhomogeneities with the statistical scaling properties of a Griffiths phase appear, and determine the spin structure of the localized impurities. The appearance of the inhomogeneities is enhanced by appropriate phonons and acts destructiv…
