Nonequilibrium Kondo Effect Research Articles

Nonequilibrium Kondo effect in a graphene-coupled quantum dot in the presence of a magnetic field.

Background: Quantum dots connected to larger systems containing a continuum of states like charge reservoirs allow the theoretical study of many-body effects such as the Coulomb blockade and the Kondo effect.Results: Here, we analyze the nonequilibrium Kondo effect and transport phenomena in a quantum dot coupled to pure monolayer graphene electrodes under external magnetic fields for finite on-site Coulomb interaction. The system is described by the pseudogap Anderson Hamiltonian. We use the equation of motion technique to determine the retarded Green’s function of the quantum dot. An analytical formula for the Kondo temperature is derived for electron and hole doping of the graphene leads. The Kondo temperature vanishes in the vicinity of the particle–hole symmetry point and at the Dirac point. In the case of particle–hole asymmetry, the Kondo temperature has a finite value even at the Dirac point. The influence of the on-site Coulomb interaction and the magnetic field on the transport properties of the system shows a tendency similar to the previous results obtained for quantum dots connected to metallic electrodes. Most remarkably, we find that the Kondo resonance does not show up in the density of states and in the differential conductance for zero chemical potential due to the linear energy dispersion of graphene. An analytical method to calculate self-energies is also developed which can be useful in the study of graphene-based systems.Conclusion: Our graphene-based quantum dot system provides a platform for potential applications of nanoelectronics. Furthermore, we also propose an experimental setup for performing measurements in order to verify our model.

Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction $U$ is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing a negative-$U$ charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. 8, 395 (2017)].

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B. We investigate the interplay between the shift () of the Kondo peak in the spin-resolved density of states (DOS) and the one () of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as only for . Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Buttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

Broken SU(4) symmetry in a Kondo-correlated carbon nanotube

This paper reports on the experimental and theoretical investigation of nonequilibrium Kondo effect in carbon nanotube quantum dots. At low temperature and in the absence of magnetic field, the authors observe two symmetric satellite features on either side of the zero bias peak due to the splitting of single-particle states by the spin-orbit coupling and valley mixing. Further experimental results are discussed based on the underlying symmetries of the carbon nanotube energy spectrum.

Anti-bias voltage electron-Kondo transport in a quantum dot device driven by a graphene sheet

Abstract We theoretically investigate the manipulation of electron-Kondo transport through a single-quantum dot (QD) two-electrode device by introducing a side-coupled graphene sheet. It is shown that with increase of coupling strength between the QD and the zero-potential graphene sheet, the anti-bias voltage capability of the QD–electrode Kondo resonance is improved obviously. This causes a high-conductance QD–electrode channel to be opened up for electron transport within a wide bias voltage range. Moreover, the conductance/current of the Kondo channel can be accurately controlled by adjusting the potential of the graphene sheet. These results may be useful for the observation of nonequilibrium Kondo effect and the design of high-conductance control device.

Improved master equation approach to quantum transport: from Born to self-consistent Born approximation.

Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U2 IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number (n)-resolved master equation (ME) approach under the self-consistent Born approximation (SCBA) for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes beyond the scope of the Born-Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise. We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.

Spin Current Generation as a Nonequilibrium Kondo Effect in a Spin–Orbit Mesoscopic Interferometer

We study nonequilibrium generation of spin-dependent transport through a single-level quantum dot embedded in a ring with the Rashba spin-orbit coupling. We consider nonmagnetic systems, involving no magnetic field nor ferromagnetic leads. It is theoretically predicted that large spin-dependent current occurs as a combined effect of the Rashba spin-orbit interaction, the Kondo effect, and nonequilibrium effect, without using magnetic field or material. The phenomenon is viewed as a new nonequilibrium correlation effect that disappears when either interaction or finite bias is absent. We show how the Kondo physics is connected with such emergent spin phenomenon by employing the finite interaction slave-boson approach.

Kondo effect in a deformed molecule coupled asymmetrically to ferromagnetic electrodes

The nonequilibrium Kondo effect is studied in a molecule quantum dot coupled asymmetrically to two ferromagnetic electrodes by employing the nonequilibrium Green function technique. The current-induced deformation of the molecule is taken into account, modeled as interactions with a phonon system, and phonon-assisted Kondo satellites arise on both sides of the usual main Kondo peak. In the antiparallel electrode configuration, the Kondo satellites can be split only for the asymmetric dot-lead couplings, distinguished from the parallel configuration where splitting also exists, even though it is for symmetric case. We also analyze how to compensate the splitting and restore the suppressed zero-bias Kondo resonance. It is shown that one can change the TMR ratio significantly from a negative dip to a positive peak only by slightly modulating a local external magnetic field, whose value is greatly dependent on the electron–phonon coupling strength.

Nonequilibrium Kondo effect and Andreev reflection through double quantum dots with spin-flip scattering

The Kondo effect and the Andreev reflection tunneling through a normal (ferromagnet)–double quantum dots–superconductor hybrid system is examined in the low temperature by using the nonequilibrium Green's function technique in combination with the slave-boson mean-field theory. The interplay of the Kondo physics and the Andreev bound state physics can be controlled by varying the interdot hopping strength. The Andreev differential conductance is mainly determined by the competition between Kondo states and Andreev states. The spin-polarization of the ferromagnetic electrode increases the zero-bias Kondo peak. The spin-flip scattering influences the Kondo effect and the Andreev reflection in a nontrivial way. For the ferromagnetic electrode with sufficiently large spin polarization, the negative Andreev differential conductance is found when the spin flip strength in the double quantum dots is sufficiently strong.

Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes

The Kondo effect is a many-body phenomenon arising due to conduction electrons scattering off a localized spin1. Coherent spin-flip scattering off such a quantum impurity correlates the conduction electrons, and at low temperature this leads to a zero-bias conductance anomaly2,3. This has become a common signature in bias spectroscopy of single-electron transistors, observed in GaAs quantum dots4,5,6,7,8,9 as well as in various single-molecule transistors10,11,12,13,14,15. Although the zero-bias Kondo effect is well established, the extent to which Kondo correlations persist in non-equilibrium situations where inelastic processes induce decoherence remains uncertain. Here we report on a pronounced conductance peak observed at finite bias voltage in a carbon-nanotube quantum dot in the spin-singlet ground state. We explain this finite-bias conductance anomaly by a non-equilibrium Kondo effect involving excitations into a spin-triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this non-equilibrium resonance.

Quantum transport from the perspective of quantum open systems

By viewing the non-equilibrium transport setup as a quantum open system, we propose a reduced-density-matrix based quantum transport formalism. At the level of self-consistent Born approximation, it can precisely account for the correlation between tunneling and the system internal many-body interaction, leading to certain novel behavior such as the non-equilibrium Kondo effect. It also opens a new way to construct time-dependent density functional theory for transport through large-scale complex systems.

Nonequilibrium Kondo effect in a quantum dot coupled to ferromagnetic leads

We study the Kondo effect in the electron transport through a quantum dot coupled to ferromagnetic leads, using a real-time diagrammatic technique that provides a systematic description of the nonequilibrium dynamics of a system with strong local electron correlations. We evaluate the theory in an extension of the ``resonant tunneling approximation,'' introduced earlier, by introducing the self-energy of the off-diagonal component of the reduced propagator in spin space. In this way we develop a charge and spin conserving approximation that accounts not only for Kondo correlations but also for the spin splitting and spin accumulation out of equilibrium. We show that the Kondo resonances, split by the applied bias voltage, may be spin polarized. A left-right asymmetry in the coupling strength and/or spin polarization of the electrodes significantly affects both the spin accumulation and the weight of the split Kondo resonances out of equilibrium. The effects are observable in the nonlinear differential conductance. We also discuss the influence of decoherence on the Kondo resonance in the frame of the real-time formulation.

Non-equilibrium Kondo Effect in Electronic Transport through Quantum Dots

Kondo effect in a quantum dot coupled to two metallic leads is studied by the non-equilibrium Green function technique. The quantum dot is described by the Anderson model with electron-electron correlations, and the corresponding Green functions are calculated by the equation of motion method. Nonlinear transport characteristics and the Kondo anomaly in differential conductance are studied in detail.

Nonequilibrium Kondo effect in a quantum dot

We present a unified theoretical approach, the finite-U slave-boson mean-field approach developed initially by Kotliar and Ruckenstein (1986 Phys. Rev. Lett. 57 1362), for the description of the linear and nonlinear Kondo-type transport through coupled double quantum dots (DQDs) connected in series to leads and through a multi-level lateral quantum dot. We find that, with increasing inter-dot hopping, the DQDs manifest three distinct physical scenarios: the Kondo singlet state of each dot with its adjacent lead, the spin singlet state consisting of local spins on each dot and the doubly occupied bonding orbital of the coupled dots. For a two-level quantum dot, our calculation demonstrates a substantial conductance enhancement near the degeneracy point of the spin singlet and triplet states, a non-monotonic temperature dependence of conductance and a sharp dip and non-zero bias maximum of the differential conductance. These agree well with recent experimental observations.

Theory of the nonequilibrium Kondo effect in a quantum dot

Based on the recent approach to the Kondo effect in a dot with a finite bias voltage by using the perturbation theory, we discuss the new peak found in the differential conductance, in addition to the zero-bias peak. The new peak originate from the splitting of the Kondo resonance under a finite voltage which may be measured by the recent proposed three-terminal quantum dot.

Nonequilibrium Kondo Effect in a Single-Channel Quantum Dot Asymmetrically Coupled to Two Ferromagnetic Reservoirs

Nonequilibrium Kondo Effect in a Single-Channel Quantum Dot Asymmetrically Coupled to Two Ferromagnetic Reservoirs

Nonequilibrium Kondo effect in quantum dots

The nonequilibrium Kondo effect in a quantum dot coupled to metallic leads is analyzed theoretically. Electron interaction on the dot is taken into account in terms of the Hubbard model for an arbitrary value of the correlation parameter U. The nonequilibrium Green function technique is used to calculate electric current and density of states. The key point of the approach is the consistency of the approximations used to calculate the lesser and retarded (advanced) Green functions. The Green functions are calculated on equal footing, i.e., within the same approximation in the framework of the equation of motion method.