We study the Kondo effect in a quantum dot which is coupled to ferromagnetic leads and analyse its properties as a function of the spin polarization of the leads. Based on a scaling approach we predict that for parallel alignment of the magnetizations in the leads the strong-coupling limit of the Kondo effect is reached at a finite value of the magnetic field. Using an equation-of-motion technique we study nonlinear transport through the dot. For parallel alignment the zero-bias anomaly may be split even in the absence of an external magnetic field. For antiparallel spin alignment and symmetric coupling, the peak is split only in the presence of a magnetic field, but shows a characteristic asymmetry in amplitude and position.PACS numbers: PACS numbers: 75.20.Hr, 72.15.Qm, 73.23.Hk The Kondo effect [1] in electron transport through a quantum dot (QD) with an odd number of electrons is experimentally well established [2, 3]. Screening of the dot spin due to the exchange coupling with lead electrons yields, at low temperatures, a Kondo resonance. The main goal of the present work is to investigate how ferromagnetic leads influence the Kondo effect. In the extreme case of half-metallic leads, minority-spin electrons are completely absent, i.e., the screening of the dot spin is not possible, and no Kondo-correlated state can form. What happens, however, for the generic case of partially spin polarized leads? How does the spin-asymmetry affect the Kondo effect? Is there still a strong coupling limit, and how are transport properties modified?Based on a poor man's scaling analysis we first show that the strong-coupling limit can still be reached in this case if an external magnetic field is applied. This is familiar from the Kondo effect in QDs with an even number of electrons [4, 5, 6, 7], which occurs at finite magnetic fields, although the physical mechanism is different in the present case. In the second part of the paper we analyze within an equation-of-motion (EOM) approach the nonlinear transport through the QD. We find that for parallel alignment of the lead magnetizations the zerobias anomaly is split. This splitting can be removed by appropriately tuning the strength of an external magnetic field B. In the antiparallel configuration of the lead magnetizations no splitting occurs at zero field.The Anderson Hamiltonian for a QD with a single level at energy ǫ 0 coupled to ferromagnetic leads iswhere c rkσ and d σ are the Fermi operators for electrons with wavevector k and spin σ in the leads, r = L, R, and in the QD, V rk is the tunneling amplitude,, and the last term is the Zeeman energy of the dot. (Stray fields from the leads are neglected.) We assume identical leads and symmetric coupling, V Lk = V Rk . The ferromagnetism of the leads is accounted for by different densities of states (DOS) ν r↑ (ω) and ν r↓ (ω) for up and down-spin electrons.In the following we study the two cases of parallel (P) and antiparallel (AP) alignment of the leads' magnetic moments. For the AP configuration and zero magnetic f...

We develop a theory of electron transport through quantum dots that are weakly coupled to ferromagnetic leads. The theory covers both the linear and nonlinear transport regime, takes noncollinear magnetization of the leads into account, and allows for an externally applied magnetic field. We derive generalized rate equations for the dot's occupation and accumulated spin and discuss the influence of the dot's spin on the transmission. A negative differential conductance and a nontrivial dependence of the conductance on the angle between the lead magnetizations are predicted.

We study resonant tunneling through a single-level quantum dot in the presence of strong Coulomb repulsion beyond the perturbative regime. The level is either spin-degenerate or can be split by a magnetic field. We, furthermore, discuss the influence of a bosonic environment. Using a real-time diagrammatic formulation we calculate transition rates, the spectral density and the nonlinear I − V characteristic. The spectral density shows a multiplet of Kondo peaks split by the transport voltage and the boson frequencies, and shifted by the magnetic field. This leads to zerobias anomalies in the differential conductance, which agree well with recent experimental results for the electron transport through single-charge traps. Furthermore, we predict that the sign of the zero-bias anomaly depends on the level position relative to the Fermi level of the leads.

We study resonant tunneling through a quantum dot with one degenerate level in the presence of a strong Coulomb repulsion and a bosonic environment. Using a real-time approach we calculate the spectral density and the nonlinear current within a conserving approximation. The spectral density shows a multiplet of Kondo peaks split by the transport voltage and boson frequencies. As a consequence we find a zero-bias anomaly in the differential conductance which can show a local maximum or minimum depending on the level position. The results are compared with recent experiments. 72.15.Qm, 73.20.Dx, 73.40.Gk, 73.50.Fq Transport phenomena through discrete energy levels in quantum dots have been studied by perturbation theory [1,2] and beyond [3][4][5]. In general, resonant tunneling phenomena and Kondo effects in nonequilibrium become important, which have been measured recently by Ralph & Buhrman [6]. In metallic islands, the Coulomb blockade is strongly influenced by inelastic interactions with bosonic degrees of freedom, such as fluctuations of the electrodynamic environment [7] or applied timedependent fields [8]. The study of inelastic interactions in quantum dots with few levels has started only recently, either for the nondegenerate case [9,10] or more general, in the presence of time-dependent fields and Coulomb blockade [2,5]. In earlier work we have studied the influence of bosonic fields in the nonequilibrium Anderson model in the perturbative regime [11] and found resonant side peaks in the Coulomb oscillations.The purpose of the present letter is to investigate the influence of external quantum-mechanical fields on transport phenomena through ultrasmall quantum dots at low temperatures and frequencies (compared to the intrinsic broadening of the resonant state in the dot). This requires a description of the Kondo effect, generalized to nonequilibrium situations and including coupling to bosonic fields. For the nonperturbative treatment of the tunneling we apply a real-time, nonequilibrium manybody approach developed recently [12,13] to a quantum dot with one level and spin degeneracy M . For M ≥ 2 and low lying dot level ǫ we obtain the usual Kondo peaks at the Fermi levels µ α of the reservoirs [4]. However, the emission of bosons causes additional Kondo singularities, for a one mode field at µ α + nω B (n = ±1, ±2, . . .).Furthermore, we will analyze the effect of the singularities in the spectral density on the differential conduc-tance as function of the bias voltage. For a low lying level we obtain the well-known zero bias maximum [4-6], whereas for a level close to the chemical potentials of the reservoirs we find a zero bias minimum. The coupling to bosons gives rise to satellite anomalies, which can be traced back to the corresponding satellite peaks in the spectral density. In a certain range of gate voltages, for M = 2 and in the absence of bosons, we find that the temperature and bias voltage dependence of the conductance coincides with recent measurements of zero-bias minima in point-contacts...