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Physical Review B

Noise of quantum dots in the ac Kondo regime: Slave-boson mean-field method and Floquet theorem

B. H. Wu, Jiafeng Cao

Published Jun 19, 2008• 7 citations
Publisher

Abstract

The noise of quantum dots in the ac Kondo regime is investigated by means of slave-boson mean-field method and Floquet theorem. A nonadiabatical formula for the noise power is obtained in the Floquet-Green formalism to take into account interaction effects. We show that, as a manifestation of many-particle correlations, the singularities of photon-assisted noise for noninteracting dots cannot survive in the ac Kondo regime. These peculiar features of the photon-assisted noise thus provide us an alternative probe to distinguish the noninteracting resonant tunneling and the many-particle Kondo resonance.

DOI
10.1103/physrevb.77.233307

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The noise of quantum dots in the ac Kondo regime is investigated by means of slave-boson mean-field method and Floquet theorem. A nonadiabatical formula for the noise power is obtained in the Floquet-Green formalism to take into account interaction effects. We show that, as a manifestation of many-particle correlations, the singularities of photon-assisted noise for noninteracting dots cannot survive in the ac Kondo regime. These peculiar features of the photon-assisted noise thus provide us an alternative probe to distinguish the noninteracting resonant tunneling and the many-particle Kondo resonance.
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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.
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 ac conductance and equilibrium current fluctuations of a Coulomb-blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite-frequency transport properties. We demonstrate that ac transport gives access to the many-body resonance in the equilibrium spectral density. It provides a new route for measuring this key signature of Kondo physics, which so far has defied direct experimental observation.
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.