We study finite-size effect of the Kondo screening cloud in a double quantum dot setup via a large-
N slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size
L and the other dot is side coupled to the embedded dot via an antiferromagnetic spin-spin-exchange coupling with a strength
K. The antiferromagnetic coupling favors local spin-singlet state and suppresses the Kondo screening. The mean-field phase diagram as a function of
1/L and
K shows a crossover to the local spin-singlet ground state from the Kondo phase to occur at
K<Kc (L=4n,4n+1,4n+3) and at
K>Kc (L=4n+2). The effective Kondo temperature
Tk (proptotional to inverse of the Kondo screening cloud size) shows the Kosterlitz-Thouless (KT) scaling at finite sizes for
L=4n,4n+2, indicating quantum transition of the KT type between the Kondo screened phase for $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with
Kc being the critical value. The local density of states on the embedded quantum dot and the persistent current at finite sizes with different values of
K are calculated in the crossover region.
The out-of-equilibrium transport properties of a double quantum dot system in the Kondo regime are studied theoretically by means of a two-impurity Anderson Hamiltonian with interimpurity hopping. The Hamiltonian is solved by means of a nonequilibrium generalization of the slave-boson mean-field theory. It is demonstrated that measurements of the differential conductance dI/dV, for appropriate values of voltages and tunneling couplings, can give a direct observation of the coherent superposition between the many-body Kondo states of each dot. For large voltages and arbitrarily large interdot tunneling, there is a critical voltage above which the physical behavior of the system again resembles that of two decoupled quantum dots.
We investigate the influence of the Fano effect on the Josephson current through a quantum dot (QD) coupled to two identical superconductors (SCs). Our attention is focused on the situation where the Kondo spin singlet survives the superconductivity and the finite- U slave-boson mean-field method is adopted to treat the Kondo correlation. With the direct coupling between the two SCs increased, the Josephson current varies in different manners in different regimes. This is consistent with the variation of Josephson coupling, which exhibits characteristics similar to those shown by the conductance through a QD connected to normal leads. But unlike the normal conductance, a negative Josephson coupling region is formed in the dip of the characteristic asymmetric peak–dip structure. Accompanying this 0–π transition, a new kind of intermediate states is found, which are different from those caused by effective ferromagnetic interaction. This 0–π transition and the intermediate states are yielded entirely by the Fano effect.
Using Wilson's numerical renormalization group (NRG) technique we compute zero-bias conductance and various correlation functions of a double quantum dot (DQD) system. We present different regimes within a phase diagram of the DQD system. By introducing a negative Hubbard U on one of the quantum dots, we simulate the effect of electron-phonon coupling and explore the properties of the coexisting spin and charge Kondo state. In a triple quantum dot (TQD) system a multi-stage Kondo effect appears where localized moments on quantum dots are screened successively at exponentially distinct Kondo temperatures.
Kondo physics in nonequilibrium interacting nanoscale devices is an attractive fundamental many-particle phenomenon with a rich potential for applications. Due to enormous complexity its clear and flexible theory is still highly desirable. We develop a physically transparent analytical theory capable of correctly describing the Kondo effect in strongly interacting systems at temperatures close to and above the Kondo temperature. We derive a nonequilibrium Keldysh field theory valid for a system with any finite electron-electron interaction which is much stronger than the coupling of the system to contacts. Finite electron-electron interactions are treated involving as many slave-boson degrees of freedom as one needs for a concrete many-body system. In a small vicinity of the zero slave-bosonic field configuration weak slave-bosonic oscillations, induced by the dot-contacts tunneling, are described by an effective Keldysh action quadratic in the slave-bosonic fields. For clarity the theory is presented for the single impurity Anderson model but the construction of the Keldysh field integral is universal and applicable to systems with more complex many-body spectra.
We study the full counting statistics (FCS) of electron tunneling through a multiterminal quantum dot in the Kondo regime within the slave-boson mean-field theory. By employing the method of Gogolin and Komnik for calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B 73, 195301 (2006)], we obtain the counting field $\ensuremath{\lambda}$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing a perturbative expansion to the first order of $\ensuremath{\lambda}$, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current autocorrelation and a positive current cross-correlation.