Session A17: Kondo Effect and Correlations in Quantum Dots

Kondo-Temperature Dependence of the Magnetic-Field Splitting of a Kondo Peak in a Single-Electron Transistor

We present a detailed study of the Kondo peak splitting as a function of Kondo temperature $T_{K}$ and magnetic field $B$ parallel to the 2DEG in an AlGaAs/GaAs single-electron transistor. We observe that, at fixed $B$, the Kondo splitting decreases logarithmically with Kondo temperature, in agreement with theory. However, we find that the magnitude of the prefactor of the logarithm is much larger than predicted. We also find that there exists a critical magnetic field $B_{c}$ below which the Kondo peak does not split, in qualitative agreement with theory. However, our results indicate that $B_{c}$ is smaller than predicted. These measurements show that the theory of non-equilibrium Kondo physics is still incomplete.   

Two-Stage Kondo effect and singlet-triplet crossover in a four-electron artificial atom

An artificial atom of 400 nm lithographic size is defined on an AlGaAs/GaAs heterostructure. With four electrons on the quantum dot, a gate-voltage-induced singlet-triplet crossover is observed. On the triplet side, a Kondo peak with a narrow dip at drain-source voltage V$_{ds}$=0 is seen. The low energy scale V$_{ds}^{\ast }$ characterizing the dip is a signature of the two-stage Kondo effect. On the singlet side, we see a Kondo enhanced feature at nonzero V$_{ds}$ due to inelastic cotunneling processes leaving the dot in the triplet excited state. The excitation energy increases as the gate voltage V$_{g}$ is tuned away from the crossover region. The effects of both the temperature T and the magnetic field B parallel to the two-dimensional electron gas are also presented. The low energy scales T$^{\ast }$ and B$^{\ast }$ are extracted from the behavior of the linear conductance and are compared to the low energy scale V$_{ds}^{\ast }$ obtained from the differential conductance.   

The Kondo effect of a magnetic impurity in an ultrasmall metallic grain

We have studied the Kondo effect of a magnetic impurity embedded in a small metallic grain with a level spacing comparable to the Kondo temperature (Kondo box). Small ($\sim $ 1nm) gold grains weakly coupled to source and drain electrodes were fabricated on top of an aluminum gate electrode using electromigration. Without magnetic impurities present, Coulomb blockade with charging energies exceeding 100 meV was observed. If cobalt impurities are introduced in the gold a gate dependent Kondo effect (T$_{k}\sim $100 K) is often observed. In many cases the Kondo peak is splitted which we attribute to the discreteness of the conduction electron spectrum of the gold grain. Temperature and magnetic field dependence contribute to a better understanding of the Kondo box. \textit{email: Hubert@qt.tn.tudelft.nl}   

Exotic Kondo States in GaAs Quantum Dots

Using a unique double quantum dot geometry, we probe an exotic Kondo effect involving one quantum dot containing excess spin-1/2 simultaneously coupled to both open and confined reservoirs of electrons. Transport measurements through open reservoirs (normal leads) reveal single channel Kondo behavior. However, the addition of a third lead consisting of a large quantum dot drastically changes transport through the other, Kondo- correlated quantum dot. We explore Kondo correlations both when Coulomb blockade confines a defined number of electrons on the large dot and when charge is allowed to fluctuate. Research supported by an NSF CAREER award DMR-0349354. RMP acknowledges support from an ARO Graduate Research Fellowship.   

Two Kondo Impurity Spin Interactions in Quantum Dots

The Kondo effect in a single quantum dot, where the localized electron behaves as a magnetic impurity, has been well studied[1]. A recent experiment by C.M. Marcus's group indicates a possible RKKY-like spin interaction between two quantum dots (QD) in the Coulomb Blockade regime.[2] We have obtained an effective Hamiltonian by carrying out a perturbation expansion (related to the Schrieffer-Wolf transformation) of an Anderson model of the two QD system (including terms representing the tunneling) to fourth order. We obtain the standard Kondo-coupling terms at second order, and we obtain RKKY-like terms at fourth order. We have also kept the scattering terms obtained at second-order, which are usually neglected, in order to study their effects on possible fixed points for the two-QD problem. We discuss the full range of interaction terms obtained at the level of RKKY, and their implications for the low-temperature behavior. {\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_}{\_} [1]Nature \textbf{391}, 156 (1998) [2]Science \textbf{304}, 565 (2004).   

Numerical evidence of tunable long-range spin interactions between quantum dots

This work was motivated by experimental results (N. J. Craig {\it et al.}, Science {\bf 304}, 565 (2004)) where two quantum dots (QDs) are connected through an open conducting region. By varying the gate potentials, a net local spin is fixed in the first QD, and the Kondo effect in the second QD is then suppressed. By either varying the gate potential in the first QD, until its net spin is zero, or by decreasing its coupling to the common conducting region, the Kondo peak in the second QD can be restored. Combining Exact Diagonalization of finite clusters with a Dyson Equation embedding procedure, we were able to reproduce these results. Two qualitatively different regimes were found: (1) When the charge in the first QD has a value of approximately 1, the conductance in the second QD has a dip where it goes exactly to zero, resembling an interference effect already noticed in previous work.$^1$ (2) When the charge in the first QD is above or bellow 1, the Kondo effect can be suppressed, but the conductance does not vanish. Work is being done on a qualitative interpretation of these results, which do not seem to support an RKKY scenario. $^1$ C. A. Busser {\it et al.}, cond-mat/0404426 (Phys. Rev. B, in press)   

Out-of-equilibrium Kondo Effect in a Three Lead Quantum Dot

We present measurements of a small GaAs quantum dot in a three lead geometry with the third lead used both as a probe of Kondo resonances and wavefunction coupling to the various reservoirs. Kondo correlations produce an enhanced density of states at the Fermi level in each reservoir. We demonstrate that the third lead probes the individual out-of-equilibrium densities of states of the two other leads when a voltage bias is fixed across them. In addition, information about the spatial distribution of quantum dot wavefunctions can be inferred from presence or absence of Coulomb blockade features in the third lead. Research supported by an NSF CARRER award DMR-0349354. RMP acknowledges support from an ARO Graduate Fellowship.   

Interference Effects in the Conductance of Multi-Level Quantum Dots

Transport properties of multilevel quantum dots are investigated in the Kondo regime. The conductance can be decomposed into the contributions of each level. It is shown that these channels can carry a different phase. A destructive interference processes are observed when the phase difference between them is $\pm\pi$.$^1$ This effect is very different from those observed in bulk metals with magnetic impurities, where the phase differences play no significant role. The effect is also different from other recent studies of interference processes in dots as the interference do not depend on external magnetic field or the hopping amplitudes dot-leads for all levels. Another interesting effect reported here is the formation of localized states that do not participate in the transport. When one of these states crosses the Fermi level, the electronic occupation of the quantum dot changes, modifying the many-body physics of the system and indirectly affecting the transport properties. $1$- C.A. B\"usser et al, cond-mat/0404426, to appears in Phys.Rev. B   

Molecular Conductors with Center of Mass Motion

We study numerically the linear conductance of a molecular conductor that can oscillate between the source and drain electrodes.$^1$ This vibrational mode leads to an asymmetric modulation of the molecule-leads hopping parameters. By expanding this modulation up to the linear order, the conductance can be decomposed into two channels, the direct hopping and the phonon-assisted tunneling channels. The Kondo regime results show conductance dips that can be attributed to the destructive interference$^2$ of these two channels. If an internal vibrational mode is also active with the effect of symmetric modulation of the tunneling barriers, the particle-hole symmetry is broken and a Fano-like interference is observed. \newline \newline $^1$ K.A. Al-Hassanieh et al - Preprint \newline $^2$ B\"usser et al, cond-mat/0404426 (to appear in Phys. Rev B).   

Spin Chain QMC simulations of Mesoscopic Quantum Impurity Models

Recent studies of quantum impurity problems have emphasized the need for flexible quantum impurity solvers. One such study focuses on mesoscopic fluctuations in the Kondo effect in quantum dots(cond-mat/0409211). Here we demonstrate that the mapping of single-quantum impurity problems to quantum spin-chains can be exploited to yield a powerful cluster algorithm that can treat the mesoscopic fluctuations exactly while at the same time being able to approach the large $D_\textrm{eff}/T$ limit with ease. The algorithm is implemented explicitly for the Anderson and Kondo Hamiltonians, and compared with standard methods for the ``mesoscopic Kondo problem.'' Using our algorithm we study mesoscopic fluctuations of the Kondo temperature in integrable and chaotic systems of various geometries.   

Noise power spectrum for tunneling through a quantum dot in the Kondo Regime

The charge-current and spin-current noise spectra are calculated for tunneling through an ultrasmall quantum dot in the Kondo regime. Modeling the dot by an infinite-U Anderson model, we use the noncrossing approximation to formulate the current-current correlation function for arbitrary frequency and voltage bias. Our formulation fulfills all the basic requirements of the current-current correlation function, including current conservation and the recovery of the fluctuation-dissipation theorem at zero frequency and bias. The full temperature, voltage-bias and frequency dependences of the noise are analyzed, and the significance of the Kondo correlations that develop are discussed. Deficiencies of the slave-boson mean-field approach for calculating the noise are pointed out.   

Unification of electromagnetic noise and Luttinger liquid via quantum-dot resonant level

We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel-coupled to a chiral Luttinger liquid (LL) with the LL parameter $K$. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance $R$, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is characterized by the effective dissipation strength $\alpha=(2\tilde{K})^{-1}$ with $\tilde{K}^{-1}=K^{-1}+2R/R_K$ and $R_K=h/e^2$ the quantum of resistance. A quantum phase transition emerges at $\tilde{K}=1/2$ and its consequences on the occupation of the level are addressed. The special limit $K=1/2^+$ is thoroughly studied at small $R/R_K$ via a link to the spin-boson-fermion model. Our result can be detected by measuring the occupation of the quantum dot or by carrying out resonant tunneling transport measurement.   

Transport properties of small Quantum rings in the Kondo regime

The possibility to construct small rings of few electrons give rise to a different physics effects.$^1$ In such systems the transport properties of quantum dots are combined with electronic interference phenomena as the Aharonov-Bohm. In this work a small quantum ring, where the Coulomb repulsion between electrons $U$ and the magnetic flux $\Phi$ are important energies scales, is studied as a function of the gate potential applied to the ring. This model can resemble all the possible effects as Kondo physics, Aharanov-Bohm effect and the degeneracy between states $k$ and $-k$. For $T=0$ the Kondo effect is present and the valley between the Coulomb peaks are fullfilled when the total charge in the ring is odd. However, there is an special case for the Coulomb blockade peak corresponding to a gate potential where the states $k$ and $-k$ are degenerated. We found that the system still in the Kondo regime even for an even charge due a $S=1$ ring's state.$^2$ When $\Phi$ is applied the degeneracy is broken destroying the $S=1$ state and eliminating the Kondo effect.$^3$ $1$- A. Fuhrer et al, Phys. Rev. Lett. {\bf 93} 176803 (2004). $2$- C.A. B\"usser et al, cond-mat/0404426, to appears in Phys.Rev. B. $3$- C.A. B\"usser, S. Ulloa, E. Dagotto and E.V. Anda (preprint).   

Transport properties of coupled quantum dots in the presence of phonons

Here is presented the numerical study of the effect of Holstein phonons in the transport properties of two coupled quantum dots (QDs) in the Kondo regime. For the QDs we use the Anderson impurity model and each QD is coupled to a different Holstein mode. At $T=0$, in the absence of phonons, and with 1 electron per dot, the usual splitting of the Kondo resonance is observed.$^1$ When the QDs are coupled to the phonons, there is a reduction of the effective Coulomb repulsion, which is explained through a canonical transformation. In addition, the conductance at the electron-hole symmetric gate potential is not affected by the phonons. This is caused by the modulation of the coupling factors.$^2$ The difference between the effects of phonons in lithographic QDs and in molecular conductors is also discussed. $1$- C.A. B\"usser et al, Phys. Rev. B {\bf 62}, 9907 (2000). $2$- K.A. Al-Hassanieh, C.A. B\"usser, G.B. Martins, Adriana Moreo and Elbio Dagotto (preprint)