Scaling and decoherence in the nonequilibrium Kondo model

We study the Kondo effect in quantum dots in an out-of-equilibrium state due to an applied dc-voltage bias. Using the method of infinitesimal unitary transformations ("flow equations"), we develop a perturbative scaling picture that naturally contains both equilibrium coherence and nonequilibrium decoherence effects. This framework allows one to study the competition between Kondo effect and current-induced decoherence, and it establishes a large regime dominated by single-channel Kondo physics for asymmetrically coupled quantum dots.     

Kondo scaling in the optical response of YbIn1-xAgxCu4

Theoretical work on Kondo systems predicts universality in the scaling of observable quantities with the Kondo temperature, T(K). Here we report infrared-frequency optical response measurements of the correlated system YbIn(1-x)AgxCu4. We observe that x-dependent variations in the frequency and strength of a low-energy excitation are related to the x-dependent Kondo temperature. Comparison of the inferred trends with existing theory and a model calculation provides a framework in which to view these experimental results as scaling phenomena arising from local-moment/conduction electron hybridization.     

Nonequilibrium Shot Noise Spectrum Through a Quantum Dot in the Kondo Regime:A Master Equation Approach under Self-Consistent Born Approximation

We construct a number(n)-resolved master equation(ME)approach under self-consistent Born approximation(SCBA)for noise spectrum calculation.The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations.We apply this approach to the challenging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum.The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach,in the sense of being applicable to the shot noise of transport under small bias voltage,in non-Markovian regime,and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.     

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

Zero-bias anomaly and kondo-assisted quasiballistic 2D transport

Nonequilibrium transport measurements in mesoscopic quasiballistic 2D electron systems show an enhancement in the differential conductance around the Fermi energy. At very low temperatures, such a zero-bias anomaly splits, leading to a suppression of linear transport at low energies. We also observed a scaling of the nonequilibrium characteristics at low energies which resembles electron scattering by two-state systems, addressed in the framework of two-channel Kondo model. Detailed sample-to-sample reproducibility indicates an intrinsic phenomenon in unconfined 2D systems in the low electron-density regime.     

Kondo-peak splitting and coherent transport in a single-electron transistor

The peculiar behavior of Kondo-peak splitting under a magnetic field and bias can be explained by calculating the nonequilibrium retarded Green's function via the nonperturbative dynamical theory (NDT). In the NDT, the application of a lead-dot-lead system reveals that new resonant tunneling levels are activated near the Fermi level and the conventional Kondo peak at the Fermi level diminishes when a bias is applied. Magnetic field causes asymmetry in the spectral density and transforms the new resonant peak into a major peak whose behavior explains all the features of the nonequilibrium Kondo phenomenon. We also show the mechanism of coherent transport through the new resonant tunneling level.     

Out-of-equilibrium Kondo effect in a mesoscopic device

We study the nonequilibrium regime of the Kondo effect in a quantum dot laterally coupled to a narrow wire. We observe a split Kondo resonance when a finite bias voltage is imposed across the wire. The splitting is attributed to the creation of a double-step Fermi distribution function in the wire. Kondo correlations are strongly suppressed when the voltage across the wire exceeds the Kondo temperature. A perpendicular magnetic field enables us to selectively control the coupling between the dot and the two Fermi seas in the wire. Already at fields of order 0.1 T only the Kondo resonance associated with the strongly coupled reservoir survives.     

Current-induced decoherence in the multichannel Kondo problem

The properties of a local spin S=1/2 coupled to K independent wires is studied in the presence of bias voltages which drive the system out of thermal equilibrium. For K?1, a perturbative renormalization group approach is employed to construct the voltage-dependent scaling function for the conductance and the T matrix. In contrast to the single-channel case, the Kondo resonance is split even by bias voltages small compared to the Kondo temperature T(K), V?T(K). Besides the applied voltage V, the current-induced decoherence rate Γ?V controls the physical properties of the system. While the presence of V changes the structure of the renormalization group considerably, decoherence turns out to be very effective in prohibiting the flow towards new nonequilibrium fixed points even in variants of the Kondo model where currents are partially suppressed.     

Measurement of quantum noise in a carbon nanotube quantum dot in the Kondo regime

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies ν of the order or higher than the frequency associated with the Kondo effect k(B)T (K)/h, with TK the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for hν ≈ k(B)T(K) a Kondo effect related singularity at a voltage bias eV ≈ hν, and a strong reduction of this singularity for hν ≈ 3k(B)T(K), in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the nonequilibrium dynamics of many-body phenomena in nanoscale devices.     

Kondo effect in quantum dots at high voltage: universality and scaling

We examine the properties of a dc-biased quantum dot in the Coulomb blockade regime. For voltages V that are large compared to the Kondo temperature T(K), the physics is governed by the scales V and gamma, where gamma approximately V/ln(2)(V/T(K)) is the nonequilibrium decoherence rate induced by the voltage-driven current. Based on scaling arguments, self-consistent perturbation theory, and perturbative renormalization group, we argue that due to the large gamma the system can be described by renormalized perturbation theory in 1/ln(V/T(K))<1. However, in certain variants of the Kondo problem, two-channel Kondo physics is induced by a large voltage V.     

Universal scaling in highly doped conducting polymer films

Electrical transport of a highly doped disordered conducting polymer, viz. poly-3,4-ethylenedioxythiophene stabilized with poly-4-styrenesulphonic acid, is investigated as a function of bias and temperature. The transport shows universal power-law scaling with both bias and temperature. All measurements constitute a single universal curve, and the complete J(V,T) characteristics are described by a single equation. We relate this scaling to dissipative tunneling processes, such as Coulomb blockade.     

Nonequilibrium quantum phase transition in itinerant electron systems

We study the effect of the voltage bias on the ferromagnetic phase transition in a one-dimensional itinerant electron system. The applied voltage drives the system into a nonequilibrium steady state with a nonzero electric current. The bias changes the universality class of the second order ferromagnetic transition. While the equilibrium transition belongs to the universality class of the uniaxial ferroelectric, we find the mean-field behavior near the nonequilibrium critical point.     

Phonon-assisted zero bias anomaly in a single-molecule quantum dot coupled to the Luttinger liquid leads

The joint effects of the electron–phonon interaction and electron–electron interaction in the Luttinger liquid leads on nonequilibrium transport through a single-molecule transistor in the Kondo regime are investigated by using the improved canonical transformation scheme and equation of motion approach. For weak intralead electron interaction, a pronounced dip around zero bias, accompanied by a series of discrete single-electron tunneling peaks is observed in the differential conductance. With the increase of the intralead interaction, the phonon-assisted peaks turn into dips, which demonstrates a phonon-assisted two-channel Kondo physics. For a certain region of interaction strength the inelastic electron tunneling can dominate electron transport. Our results well explain the experiments of zero bias anomaly.     

Evolution of the Kondo effect in a quantum dot probed by shot noise

We measure the current and shot noise in a quantum dot in the Kondo regime to address the nonequilibrium properties of the Kondo effect. By systematically tuning the temperature and gate voltages to define the level positions in the quantum dot, we observe an enhancement of the shot noise as temperature decreases below the Kondo temperature, which indicates that the two-particle scattering process grows as the Kondo state evolves. Below the Kondo temperature, the Fano factor defined at finite temperature is found to exceed the expected value of unity from the noninteracting model, reaching 1.8±0.2.     

Probing the Kondo density of states in a three-terminal quantum ring

We have measured the Kondo effect in a quantum ring connected to three terminals. In this configuration nonlinear transport measurements allow us to check which lead contributes to the Kondo density of states (DOS) and which does not. The ring geometry allows a fine-tuning of the coupling to each lead through the Aharonov-Bohm effect via application of a magnetic field. When the ring is connected to two strongly and one weakly coupled leads, conductance through the weakly coupled lead provides a direct measurement of the DOS in the Kondo regime. By applying a bias between the two strongly coupled leads, we demonstrate directly the splitting of the out-of-equilibrium Kondo DOS.     

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.     

SU(4) Kondo effect in carbon nanotubes

We investigate theoretically the nonequilibrium transport properties of carbon nanotube quantum dots. Owing to the two-dimensional band structure of graphene, a double orbital degeneracy plays the role of a pseudospin, which is entangled with the spin. Quantum fluctuations between these 4 degrees of freedom result in an SU(4) Kondo effect at low temperatures. This exotic Kondo effect manifests as a four-peak splitting in the nonlinear conductance when an axial magnetic field is applied.     

Nonequilibrium spintronic transport through an artificial Kondo impurity: conductance,magnetoresistance, and shot noise

We investigate the nonequilibrium transport properties of a quantum dot when spin flip processes compete with the formation of a Kondo resonance in the presence of ferromagnetic leads. Based upon the Anderson Hamiltonian in the strongly interacting limit, we predict a splitting of the differential conductance when the spin flip scattering amplitude is of the order of the Kondo temperature. We discuss how the relative orientation of the lead magnetizations strongly influences the electronic current and the shot noise in a nontrivial way. Furthermore, we find that the zero-bias tunneling magnetoresistance becomes negative with increasing spin flip scattering amplitude.     

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.