Kondo Effect In Quantum Dots Research Articles

Kondo effect and spin\u2013orbit coupling in graphene quantum dots

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction.

Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs

We elaborate on the recently introduced concept of reentrant Kondo effect in quantum impurities/dots coupled to hybrid metal-semiconductor contacts [G.~Diniz {\em et al.}, Phys. Rev. B {\bf 101}, 125115 (2020)]. By noticing the equivalence of the originally suggested semiconducting arrangement to an analogous three-terminal quantum dot setup with a normal and two phase-biased superconducting leads introduced in our recent work [Phys. Rev. B {\bf 103}, 035419 (2021)], we put this effect into a new physical context, which enables us a fresh look on the problem. First, we identify the superconducting counterpart of the reentrant Kondo effect and, consequently, reveal its fragility with respect to an underlying doublet-singlet quantum phase transition induced by the particle-hole asymmetry of the reservoir densities of states. This is pertinent (even if previously unnoticed) also in the original as well as extended semiconducting setups, where it puts stringent conditions on the symmetry of the contact density of states. Furthermore, we analyze experimental feasibility of observing the reentrant Kondo effect in its superconducting realization concluding that even present day experiments might see the onset of the reentrant behavior, but fully developed Kondo features cannot be reached due to the required vast separation of energy/temperature scales.

Kondo-like zero-bias conductance anomaly in a three-dimensional topological insulator nanowire.

Zero-bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero-bias peaks in nanowires—for example, weak localization, Andreev bound states, or the Kondo effect. Here, we discuss observations of differential-conductance peaks at zero-bias voltage in non-superconducting electronic transport through a 3D topological insulator (Bi1.33Sb0.67)Se3 nanowire. The zero-bias conductance peaks show logarithmic temperature dependence and often linear splitting with magnetic fields, both of which are signatures of the Kondo effect in quantum dots. We characterize the zero-bias peaks and discuss their origin.

Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts

Quantum point contacts are narrow, one-dimensional constrictions usually patterned in a two-dimensional electron system, for example by applying voltages to local gates. The linear conductance of a point contact, when measured as function of its channel width, is quantized in units of GQ = 2e(2)/h, where e is the electron charge and h is Planck's constant. However, the conductance also has an unexpected shoulder at ∼0.7GQ, known as the '0.7-anomaly', whose origin is still subject to debate. Proposed theoretical explanations have invoked spontaneous spin polarization, ferromagnetic spin coupling, the formation of a quasi-bound state leading to the Kondo effect, Wigner crystallization and various treatments of inelastic scattering. However, explicit calculations that fully reproduce the various experimental observations in the regime of the 0.7-anomaly, including the zero-bias peak that typically accompanies it, are still lacking. Here we offer a detailed microscopic explanation for both the 0.7-anomaly and the zero-bias peak: their common origin is a smeared van Hove singularity in the local density of states at the bottom of the lowest one-dimensional subband of the point contact, which causes an anomalous enhancement in the Hartree potential barrier, the magnetic spin susceptibility and the inelastic scattering rate. We find good qualitative agreement between theoretical calculations and experimental results on the dependence of the conductance on gate voltage, magnetic field, temperature, source-drain voltage (including the zero-bias peak) and interaction strength. We also clarify how the low-energy scale governing the 0.7-anomaly depends on gate voltage and interactions. For low energies, we predict and observe Fermi-liquid behaviour similar to that associated with the Kondo effect in quantum dots. At high energies, however, the similarities between the 0.7-anomaly and the Kondo effect end.

Detection of a Charged Two-Level System by Using the Kondo and the Fano–Kondo Effects in Quantum Dots

The Kondo effect and the Fano–Kondo effect are important phenomena that have been observed in quantum dots (QDs). We theoretically investigate the transport properties of a coupled QD system in order to study the possibility of detecting a qubit state from the modulation of the conductance peak in the Kondo effect and the dip in the Fano–Kondo effect. We show that the peak and dip of the conductance are both shifted depending on the qubit state. In particular, we find that we can estimate the optimal point and tunneling coupling between the |0> and |1> states of the qubit by measuring the shift of the positions of the conductance peak and dip, as functions of the applied gate voltage on the qubit and the distance between the qubit and the detector.

Universality of the Kondo Effect in Quantum Dots with Ferromagnetic Leads

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. Most of the Kondo resonances exhibit a splitting, which depends on the tunnel coupling to the leads and an external magnetic field B, but only weakly on the gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on gμ(B)(B-B(c))/k(B)T(K), where T(K) is the Kondo temperature and B(c) the external field compensating the splitting.

Slave-boson Keldysh field theory for the Kondo effect in quantum dots

We present a {\it nonequilibrium nonperturbative} field theory for the Kondo effect in strongly interacting quantum dots at finite temperatures. Unifying the slave-boson representation with the Keldysh field integral an effective Keldysh action is derived and explored in the vicinity of the zero slave-bosonic field configuration. The theory properly reflects the essential features of the Kondo physics and at the same time significantly simplifies a field-theoretic treatment of the phenomenon, avoiding complicated saddle point analysis or 1/N expansions, used so far. Importantly, our theory admits a {\it closed analytical} solution which explains the mechanism of the Kondo effect in terms of an interplay between the real and imaginary parts of the slave-bosonic self-energy. It thus provides a convenient nonperturbative building block, playing the role of a "free propagator", for more advanced theories. We finally demonstrate that already this simplest possible field theory is able to correctly reproduce experimental data on the Kondo peak observed in the differential conductance, correctly predicts the Kondo temperature and, within its applicability range, has the same universal temperature dependence of the conductance as the one obtained in numerical renormalization group calculations.

Underscreened Kondo effect in quantum dots coupled to ferromagnetic leads

We analyze the equilibrium transport properties of underscreened Kondo effect in the case of a two-level quantum dot coupled to ferromagnetic leads. Using the numerical renormalization-group (NRG) method, we have determined the gate voltage dependence of the dot's spin and level-resolved spectral functions. We have shown that the polarization of the dot is very susceptible to spin imbalance in the leads and changes sign in the middle of the $S=1$ Coulomb valley. Furthermore, we have also found that by fine tuning an external magnetic field one can compensate for the presence of ferromagnetic leads and restore the Kondo effect in the case of $S=\frac{1}{2}$ Coulomb valley. The underscreened Kondo effect is, however, extremely sensitive to the magnetic field which hinders the full restoration of the Kondo peak.

Magnetic flux and gate-voltage dependence of Kondo effect in quantum dot embedded in Aharonov–Bohm ring

The Kondo effect is examined in a quantum dot embedded in an Aharonov–Bohm (AB) ring, based on the Haldane's two-stage scaling theory. In the small limit of the ring size, we derive analytical expressions for the Kondo temperature T K and conductance at temperatures T ⪢ T K , as functions of the magnetic flux penetrating the ring. The flux dependence of T K is drastically changed when the energy level in the quantum dot is tuned electrostatically using the gate electrode attached to the dot. T K hardly depends on the flux at the midpoint in the Kondo valley of the Coulomb oscillation, whereas its flux dependence becomes remarkable apart from the midpoint.

Multiorbital Kondo effect in quantum dots coupled to ferromagnetic leads

We investigate the Kondo effect of a multiorbital quantum dot coupled to ferromagnetic leads, using an equation of motion method. It is shown that the Kondo peak splits into three peaks and the middle one is located close to the Fermi energy. As the spin polarization of the leads is increased, the splitting between the highest and lowest energy peaks increases. The results indicate that the Kondo effect caused by the orbital degrees of freedom remains, while the Kondo effect caused by the spin degrees of freedom is suppressed. The origin of the suppressed spin Kondo effect is discussed in terms of the renormalized energy level of the quantum dot.

Scaling Analysis for Kondo Effect in Quantum Dot Embedded in Aharonov–Bohm Ring

The Kondo effect is theoretically studied in a quantum dot embedded in an Aharonov–Bohm (AB) ring when the size of the ring is much smaller than the Kondo cloud. First, we construct an equivalent model in which a quantum dot is coupled to a single lead. The AB interference effect is involved in the magnetic-flux dependence of the density of states in the lead. The scaling analysis of this model yields analytical expressions for the Kondo temperature T K and conductance at temperatures T ≫ T K . We show that T K may be significantly modulated by the magnetic flux penetrating the ring. Our method is generally applicable to the investigation of the Kondo effect in mesoscopic complex systems including a quantum dot.

Interplay between particle-hole splitting and the Kondo effect in quantum dots

We discuss the influence of proximity effect on the quantum dot located between metallic and superconducting electrodes and consider its interplay with the Kondo state arising from the on-dot correlations. We show that upon increasing the hybridization to superconducting lead the Kondo resonance is gradually washed out. This behavior indirectly affects the subgap charge transport suppressing the zero-bias enhancement of the Andreev conductance.

The Kondo effect in quantum dots coupled to ferromagnetic leads with noncollinearmagnetizations: effects due to electron–phonon coupling

Spin-polarized transport through a quantum dot strongly coupled to ferromagneticelectrodes with noncollinear magnetic moments is analysed theoretically in terms of thenonequilibrium Green function formalism based on the equation of motion method.Electrons in the dot are assumed to be coupled to a phonon bath. The influence ofelectron–phonon coupling on tunnelling current, linear and nonlinear conductance, andtunnel magnetoresistance is studied in detail. Variation of the main Kondo peaks andphonon satellites with the angle between the magnetic moments of the leads isanalysed.

Compensation of the Kondo effect in quantum dots coupled to ferromagnetic leads withinthe equation of motion approach

We propose a new approximation scheme within the equation of motion approach (EOM)to spin polarized transport through a quantum dot coupled to ferromagneticleads. It has some advantages over a standard EOM technique widely used inthe literature, in particular when we are interested in spin polarized quantities.Namely, it gives values of the dot spin polarization which are closer to the onesobtained within the numerical renormalization group (NRG) than the standardEOM approach. While restoring the Kondo effect, the spin polarization vanishesand the transport becomes unpolarized, in agreement with NRG and real timediagrammatic calculations. The standard EOM procedure gives non-zero values of the spinpolarization, and the transport is still spin polarized. Both approximations give the samecorrect splitting of the Kondo peaks due to ferromagnetism in the electrodes.

Spin splitting and Kondo effect in quantum dots coupled to noncollinear ferromagnetic leads

We study the Kondo effect in a quantum dot coupled to two noncollinear ferromagnetic leads. First, we study the spin splitting $\delta\epsilon=\epsilon_{\downarrow}-\epsilon_{\uparrow}$ of an energy level in the quantum dot by tunnel couplings to the ferromagnetic leads, using the Poor man's scaling method. The spin splitting takes place in an intermediate direction between magnetic moments in the two leads. $\delta\epsilon \propto p\sqrt{\cos^2(\theta/2)+v^2\sin^2(\theta/2)}$, where $p$ is the spin polarization in the leads, $\theta$ is the angle between the magnetic moments, and $v$ is an asymmetric factor of tunnel barriers ($-1<v<1$). Hence the spin splitting is always maximal in the parallel alignment of two ferromagnets ($\theta=0$) and minimal in the antiparallel alignment ($\theta=\pi$). Second, we calculate the Kondo temperature $T_{\mathrm{K}}$. The scaling calculation yields an analytical expression of $T_{\mathrm{K}}$ as a function of $\theta$ and $p$, $T_{\mathrm{K}}(\theta, p)$, when $\delta\epsilon \ll T_{\mathrm{K}}$. $T_{\mathrm{K}}(\theta, p)$ is a decreasing function with respect to $p\sqrt{\cos^2(\theta/2)+v^2\sin^2(\theta/2)}$. When $\delta\epsilon$ is relevant, we evaluate $T_{\mathrm{K}}(\delta\epsilon, \theta, p)$ using the slave-boson mean-field theory. The Kondo resonance is split into two by finite $\delta\epsilon$, which results in the spin accumulation in the quantum dot and suppression of the Kondo effect.

Interplay of electromagnetic noise and Kondo effect in quantum dots

We investigate the influence of an electromagnetic environment, characterized by a finite impedance $Z(\omega)$, on the Kondo effect in quantum dots. The circuit voltage fluctuations couple to charge fluctuations in the dot and influence the spin exchange processes transferring charge between the electrodes. We discuss how the low-energy properties of a Kondo quantum dot subject to dynamical Coulomb blockade resemble those of Kondo impurities in Luttinger liquids. Using previous knowledge based on the bosonization of quantum impurity models, we show that low-voltage conductance anomalies appear at zero temperature. The conductance can vanish at low temperatures even in presence of a screened impurity spin. Moreover, the quantitative determination of the corresponding Kondo temperature depends on the full frequency-dependent impedance of the circuit. This is demonstrated by a weak-coupling calculation in the Kondo interaction, taking into account the full distribution $P(E)$ of excited environmental modes.

Kondo effect with noncollinear polarized leads: A numerical renormalization group analysis

The Kondo effect in quantum dots attached to ferromagnetic leads with general polarization directions is studied combining poor man scaling and Wilson's numerical renormalization group methods. We show that polarized electrodes will lead in general to a splitting of the Kondo resonance in the quantum dot density of states except for a small range of angles close to the antiparallel case. We also show that an external magnetic field is able to compensate this splitting and restore the unitary limit. Finally, we study the electronic transport through the device in various limiting cases.

Modulation of three‐orbital Kondo effect in quantum dots

We study the orbital Kondo effect due to two electrons occupying three orbital levels in quantum dot (QD) systems. By applying the non-crossing approximation to the three-orbital Anderson impurity model, we calculate the conductance and the thermopower. We consider the realistic situation in QD systems, where the correlation effect induces the orbital-level splitting even at zero field. It is found that the level splitting at zero field larger than temperature revives the maximum structure in the conductance clearly, which characterizes the singlet-triplet Kondo effect. We also show that the enhancement of the Kondo temperature due to the singlet-triplet mechanism gives rise to the characteristic behavior in the thermopower as well. This is in contrast with the two-orbital case, where the thermopower is zero irrespective of the level splitting. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Residual Kondo effect in quantum dot coupled to half-metallic ferromagnets

We study the Kondo effect in a quantum dot coupled to half-metallic ferromagneticelectrodes in the regime of strong on-dot correlations. Using the equation of motiontechnique for non-equilibrium Green functions in the slave boson representation, we showthat the Kondo effect is not completely suppressed for anti-parallel magnetization of theleads. In the parallel configuration, there is no Kondo effect but there is an effect associatedwith elastic co-tunnelling which, in turn, leads to similar behaviour of the local (on-dot)density of states (LDOS) as the usual Kondo effect. Namely, the LDOS shows thetemperature-dependent resonance at the Fermi energy, which splits with the bias voltageand the magnetic field. Moreover, unlike for non-magnetic or not fully polarizedferromagnetic leads, only the minority spin electrons can form such resonance in thedensity of states. However, this resonance cannot be observed directly in the transportmeasurements, and we give some clues how to identify the effect in such systems.

Kondo effect in quantum dots coupled to ferromagnetic leads with noncollinear magnetizations

Non-equilibrium Green's function technique has been used to calculate spin-dependent electronic transport through a quantum dot in the Kondo regime. The dot is described by the Anderson Hamiltonian and is coupled either symmetrically or asymmetrically to ferromagnetic leads, whose magnetic moments are noncollinear. It is shown that the splitting of the zero bias Kondo anomaly in differential conductance decreases monotonically with increasing angle between magnetizations, and for antiparallel configuration it vanishes in the symmetrical case while remains finite in the asymmetrical one.