Nonequilibrium Keldysh formalism for interacting leads—Application to quantum dot transport driven by spin bias

The conductance through a mesoscopic system of interacting electrons coupled to two adjacent leads is conventionally derived via the Keldysh nonequilibrium Green’s function technique, in the limit of noninteracting leads [Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68 (1992) 2512]. We extend the standard formalism to cater for a quantum dot system with Coulombic interactions between the quantum dot and the leads. The general current expression is obtained by considering the equation of motion of the time-ordered Green’s function of the system. The nonequilibrium effects of the interacting leads are then incorporated by determining the contour-ordered Green’s function over the Keldysh loop and applying Langreth’s theorem. The dot–lead interactions significantly increase the height of the Kondo peaks in density of states of the quantum dot. This translates into two Kondo peaks in the spin differential conductance when the magnitude of the spin bias equals that of the Zeeman splitting. There also exists a plateau in the charge differential conductance due to the combined effect of spin bias and the Zeeman splitting. The low-bias conductance plateau with sharp edges is also a characteristic of the Kondo effect. The conductance plateau disappears for the case of asymmetric dot–lead interaction.     

Singlet-triplet transition in a quantum dot: effect on mesoscopic transport

The T=0 transport properties of a wire interacting with a lateral two-level quantum dot are studied by using an exact numerical calculation. The wire conductance, the spin–spin correlation and the Kondo temperature are obtained as a function of the dot level energy spacing. When the dot has two electrons and spin S_D1, the wire current is totally quenched by the S=1 Kondo effect. The Kondo temperature is maximum at the singlet–triplet transition and its dependence upon the dot energy spacing follows a non-universal scaling law.     

Universal scaling in nonequilibrium transport through a single channel Kondo dot

Scaling laws and universality play an important role in our understanding of critical phenomena and the Kondo effect. We present measurements of nonequilibrium transport through a single-channel Kondo quantum dot at low temperature and bias. We find that the low-energy Kondo conductance is consistent with universality between temperature and bias and is characterized by a quadratic scaling exponent, as expected for the spin-1/2 Kondo effect. We show that the nonequilibrium Kondo transport measurements are well described by a universal scaling function with two scaling parameters.     

Spin filters with Fano dots

We compute the zero bias conductance of electrons through a single ballistic channel weakly coupled to a side quantum dot with Coulomb interaction. In contrast to the standard setup which is designed to measure the transport through the dot, the channel conductance reveals Coulomb blockade dips rather then peaks due to the Fano-like backscattering. At zero temperature the Kondo effect leads to the formation of broad valleys of small conductance corresponding to an odd number of electrons on the dot. By applying a magnetic field in the dot region we find two dips corresponding to a total suppression in the conductance of spins up and down separated by an energy of the order of the Coulomb interaction. This provides a possibility of a perfect spin filter.Received: 6 November 2003, Published online: 2 April 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 73.23.Ad Ballistic transport - 72.25.-b Spin polarized transport     

Spin fractionalization of an even number of electrons in a quantum Dot

We find that Kondo resonant conductance can occur in a quantum dot in the Coulomb blockade regime with an even number of electrons N. The contacts are attached to the dot in a pillar configuration, and a magnetic field B( perpendicular) along the axis is applied. B( perpendicular) lifts the spin degeneracy of the dot energies. Usually, this prevents the system from developing the Kondo effect. Tuning B( perpendicular) to the value B(*) where levels with different total spin cross restores both the degeneracy and the Kondo effect. We analyze a dot charged with N = 2 electrons. Coupling to the contacts is antiferromagnetic due to a spin selection rule and, in the Kondo state, the charge is unchanged while the total spin on the dot is S = 1/2.     

Entanglement and transport through correlated quantum dot

We study quantum entanglement in a single-level quantum dot in the linear-response regime. The results show, that the maximal quantum value of the conductance 2e²/h not always match the maximal entanglement. The pairwise entanglement between the quantum dot and the nearest atom of the lead is also analyzed by utilizing the Wootters formula for charge and spin degrees of freedom separately. The coexistence of zero concurrence and the maximal conductance is observed for low values of the dot-lead hybridization. Moreover, the pairwise concurrence vanish simultaneously for charge and spin degrees of freedom, when the Kondo resonance is present in the system. The values of a Kondo temperature, corresponding to the zero-concurrence boundary, are also provided.     

Spin-Polarized Transport Through a Quantum Dot Coupled to Ferromagnetic Leads:Kondo Correlation Effect

We investigate the linear and nonlinear transport through a single level quantum dot connected to two ferromagnetic leads in Kondo regime, using the slave-boson mean-field approach for finite on-site Coulomb repulsion. We find that for antiparallel alignment of the spin orientations in the leads, a single zero-bias Kondo peak always appears in the voltage-dependent differential conductance with peak height going down to zero as the polarization grows to P=1. For parallel configuration, with increasing polarization from zero, the Kondo peak descends and greatly widens with the appearance of shoulders, and finally splits into two peaks on both sides of the bias voltage around P～0.7 until disappearing at even larger polarization strength. At any spin orientation angle θ, the linear conductance generally drops with growing polarization strength. For a given finite polarization, the minimum linear conductance always appears at θ=π.     

Spin polarized Kondo transport through a quantum dot connected to ferromagnetic leads

We study the spin dependent transport through a quantum dot connected to ferromagnetic leads. Using the non-equilibrium generalization of the non-crossing approximation for finite Coulomb repulsion U, we compute the spin polarized conductance, the local average occupancies and the local densities of states in the Kondo regime. We show that transport properties are strongly affected if we allow double occupancy by using a finite value for U. In the framework of our model, we have successfully reproduced the recent experimental finding of an electrically controlled magnetic moment on a carbon nanotube quantum dot coupled to ferromagnetic nickel leads [3]. Besides, in addition to the well known splitting of the Kondo peak in the density of states due to the presence of ferromagnetic leads, we find that the additional splitting due to non-zero bias voltage leads to an unexpected increase of the total conductance, which has also been observed by Hauptmann et al.     

Transport through artificial single-molecule magnets: Spin-pair state sequential tunneling and Kondo effects

The transport properties of an artificial single-molecule magnet based on a CdTe quantum dot doped with a single Mn+2 ion(S=5/2) are investigated by the non-equilibrium Green function method.We consider a minimal model where the Mn-hole exchange coupling is strongly anisotropic so that spin-flip is suppressed and the impurity spin S and a hole spin s entering the quantum dot are coupled into spin pair states with(2S+1) sublevels.In the sequential tunneling regime,the differential conductance exhibits(2S+1) possible peaks,corresponding to resonance tunneling via(2S+1) sublevels.At low temperature,Kondo physics dominates transport and(2S+1) Kondo peaks occur in the local density of states and conductance.These peaks originate from the spin-singlet state formed by the holes in the leads and on the dot via higher-order processes and are related to the parallel and antiparallel spin pair states.     

Spin-flip Fano–Kondo resonant tunneling through a quantum dot interferometer responded by a rotating magnetic field

The Fano and Kondo cooperated resonant tunneling through a quantum dot interferometer under the perturbation of a rotating magnetic field is investigated theoretically. The spin-polarized current components have been derived generally by employing the Keldysh nonequilibrium Green?s function method, through which the charge and spin currents are determined directly. The numerical calculations on spin and charge currents are performed to show the compound features of mesoscopic transport associated with the Kondo, Fano, and Zeeman effects intimately. The induced spin current in the Kondo regime is much different from the one in the non-interacting regime. The spin current is tuned from resonant peak to valley by varying external parameters.     

Charge distribution in a Kondo-correlated quantum dot

We report on direct measurement of charge and its distribution in a Kondo correlated quantum dot (QD). A noninvasive potential-sensitive detector, in proximity with a QD, reveals that, although the conductance of the QD is significantly enhanced as it enters the Kondo regime, the average charge remains unaffected. This demonstrates the separation between spin and charge degrees of freedom. We find, however, under certain conditions, an abrupt redistribution of charge in the QD, taking place with an onset of Kondo correlation. This suggests a correlation between the spin and charge degrees of freedom.     

Multipeak Kondo effect in one- and two-electron quantum dots

We have fabricated a few-electron quantum dot that can be tuned down to zero electrons while maintaining strong coupling to the leads. Using a nearby quantum point contact as a charge sensor, we can determine the absolute number of electrons in the quantum dot. We find several sharp peaks in the differential conductance, occurring at both zero and finite source-drain bias, for the one- and two-electron quantum dot. We attribute the peaks at finite bias to a Kondo effect through excited states of the quantum dot and investigate the magnetic field dependence of these Kondo resonances.     

T型双量子点分子Aharonov-Bohm干涉仪的电输运

利用非平衡格林函数方法, 理论研究T型双量子点分子Aharonov-Bohm (A-B)干涉仪的电荷及其自旋输运性质. 通过控制T型双量子点分子内量子点间有无耦合, 能够实现在同一电子能级位置处分别出现共振和反共振状态, 根据此性质, 能将体系设计成量子开关器件. 当将两个完全相同的T型双量子点分子分别嵌入A-B干涉仪两臂中时, 磁通取适当数值, 能够出现完全的量子相消干涉. 通过调节量子点能级、左右两电极间的偏压和Rashba自旋轨道相互作用强度, 可对体系自旋流进行调控. 关键词： 非平衡格林函数 T型双量子点分子 Aharonov-Bohm干涉仪 自旋输运     

Influence of inter-dot Coulomb repulsion and exchange interactions on conductance through double quantum dot

Conductance and other physical quantities are calculated in double quantum dots (DQD) connected in series in the limit of coherent tunnelling using a Green's function technique. The inter-dot Coulomb repulsion and the exchange interaction are studied by means of the Kotliar and Ruckenstein slave-boson mean-field approach. The crossover from the atomic to the molecular limit is analyzed in order to show how the conductance in the model depends on the competition between the level broadening (dot-lead coupling) and the dot-dot transmission. The double Kondo effect was found in the gate voltage characteristics of the conductance in the atomic limit. In the case, when each dot accommodates one electron, the Kondo resonant states are formed between dots and their adjacent leads and transport is dominated by hopping between these two resonances. In the molecular limit the conductance vanishes for sufficiently low gate voltages, which means the Kondo effect disappeared. For small dot-lead coupling the transport characteristics are very sensitive on the influence of the inter-dot Coulomb repulsion and the position of the local energy level. The resonance region is widened with increase of the inter-dot Coulomb interactions while the exchange interaction has opposite influence.     

Kondo effect in the presence of magnetic impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.     

Interaction-driven spin precession in quantum-dot spin valves

We analyze spin-dependent transport through spin valves composed of an interacting quantum dot coupled to two ferromagnetic leads. The spin on the quantum dot and the linear conductance as a function of the relative angle theta of the leads' magnetization directions is derived to lowest order in the dot-lead coupling strength. Because of the applied bias voltage spin accumulates on the quantum dot, which for finite charging energy experiences a torque, resulting in spin precession. The latter leads to a nontrivial, interaction-dependent, theta dependence of the conductance. In particular, we find that the spin-valve effect is reduced for all theta not equal pi.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

Tunability of the Kondo effect in an asymmetrically tunnel coupled quantum dot

The transport properties of a single quantum dot were measured at low temperature in a regime of strong asymmetric tunnel coupling to leads. By tuning this asymmetry, the two parameters of the Kondo effect in a quantum dot, the Kondo temperature and the zero-bias zero-temperature conductance, were independently controlled. A careful analysis of the Coulomb energies and of the tunnel couplings was performed. It allowed an estimate of the Kondo temperature independently of its value obtained via the temperature dependence of the conductance. Both are in good agreement. We finally compared our experimental data with an exact solution of the Kondo problem which provides the dependence of the differential conductance on temperature and source-drain voltage. Theoretical expectations fit quite well our experimental data in the equilibrium and out-of-equilibrium regimes.     

Tunable Kondo effect in a double quantum dot coupled to ferromagnetic contacts

We investigate the effects induced by ferromagnetic contacts attached to a serial double quantum dot. Spin polarization generates effective magnetic fields and suppresses the Kondo effect in each dot. The superexchange interaction J(AFM), tuned by the interdot tunneling rate t, can be used to compensate the effective fields and restore the Kondo resonance when the contact polarizations are aligned. As a consequence, the direction of the spin conductance can be controlled and even reversed using electrostatic gates alone. Our results demonstrate a new approach for controlling spin-dependent transport in carbon nanotube double dot devices.     

Orbital Kondo effect in cobalt-benzene sandwich molecules

We study a Co-benzene sandwich molecule bridging the tips of a Cu nanocontact as a realistic model of correlated molecular transport. To this end we employ a recently developed method for calculating the correlated electronic structure and transport properties of nanoscopic conductors. When the molecule is slightly compressed by the tips of the nanocontact the dynamic correlations originating from the strongly interacting Co 3d shell give rise to an orbital Kondo effect while the usual spin Kondo effect is suppressed due to Hund's rule coupling. This nontrivial Kondo effect produces a sharp and temperature-dependent Abrikosov-Suhl resonance in the spectral function at the Fermi level and a corresponding Fano line shape in the low bias conductance.