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(a) Cross-section of rectangular quantum dot. The semiconductor material consists of an undoped AlGaAs(7nm)/InGaAs(12nm)/AlGaAs(7nm) double barrier structure sandwiched between n-doped GaAs source and drain electrodes. A gate electrode surrounds the pillar and is used to control the electrostatic confinement in the quantum dot. A dc bias voltage, V , is applied between source and drain and current, I, flows vertically through the pillar. The gate voltage, Vg, can change the number of confined electrons, N , one-by-one. A magnetic field, B, is applied along the vertical axis. (b) Scanning electron micrograph of a quantum dot with dimensions 0.45 × 0.6 µm 2 and height of ∼ 0.5 µm.
Source publication
We review the peculiarities of transport through a quantum dot caused by the spin transition in its ground state. Such transitions can be induced by a magnetic field. Tunneling of electrons between the dot and leads mixes the states belonging to the ground state manifold of the dot. Unlike the conventional Kondo effect, this mixing, which occurs on...
Context in source publication
Context 1
... quantum dot has the external shape of a rect- angular pillar (see Fig. 5) and an internal confinement potential close to a two-dimensional ellipse [8]. The tun- nel barriers between the quantum dot and the source and drain electrodes are thinner than in other devices such that higher-order tunneling processes are enhanced. Fig. 6 shows the linear response conductance G versus gate voltage V g , and magnetic ...
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We study a small spin-degenerate quantum dot with even number of electrons, weakly connected by point contacts to the metallic electrodes, and subject to an external magnetic field. If the Zeeman energy B is equal to the single-particle level spacing $\Delta $ in the dot, the ground state of the dot becomes doubly degenerate, and the system exhibit...
The cotunneling spectroscopy through quantum dots containing one, two, and three electrons was experimentally investigated. Inelastic cotunneling was used to measure the two-electron singlet-triplet (ST) splitting above and below a magnetic field driven singlet-triplet transition. Evidence of a nonequilibrium ST Kondo effect for two electrons was p...
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Citations
... The Kondo effect originally refers to a minimum of the resistance as a function of temperature in a metal [170] due to scattering off magnetic impurities, where the impurity and the electron exchange their spin. Nowadays, the Kondo effect is mainly studied in quantum dots and carbon nanotubes [168,[171][172][173][174][175][176][177][178][179][180][181][182][183][184][185][186][187][188] and became a test case for many-body theories in condensed matter physics [189][190][191][192][193][194][195][196]. ...
(English)
During the last decades, semiclassical techniques for single particle systems have been successfully developed, to the point that they describe the universal and reproducible quantum fluctuations characteristic of quantum systems with chaotic classical limit. By now they not only give a qualitative and intuitive picture about interference, but also yield quantitatively good results.
Motivated by this story of success, the aim of this thesis was to first of all rigorously deduce a semiclassical theory for many-body systems in Fock space from path integrals, thus pushing the work of John Hasbrouck Van Vleck, Richard Feynman, Martin Charles Gutzwiller and Michael Victor Berry to the next level. The central object in this development is the propagator in Fock basis, for which a path integral in complex variables has to be found, from which the corresponding classical theory can be deduced. The main focus of attention there lies the action of the classical trajectories being real thus supporting the explicit, illustrative and manifest study of many-body interference.
Then, with the help of this semiclassical propagator, universal many-body interference effects in bosonic and fermionic Fock space are studied several of which are novel predictions due to new qualitative tools developed here. The semiclassical tool for quantum fields, and the picture of many-body interference it provides, is put to test against numerical calculations. For a quantitative comparison, the loop expansion developed by Martin Sieber and Klaus Richter going beyond Michael Berry's diagonal approximation is transfered and adopted to the theory in Fock space. All our predictions then show excellent agreement with quantum mechanical simulations.
... The conduction mechanism for the Kondo effect involves spin-flip events such as the one illustrated in figure 3.4. We refer to other papers [40][41][42][43][44][45] for a more detailed theoretical discussion. Here, we concentrate on its main transport characteristics, which are summarized in figures 3.5 and 3.6. ...
Transport through single molecules has been studied using different test beds. In this
paper we focus on three-terminal devices in which a molecule bridges the gap
between two gold electrodes and a third electrode—the gate—is able to modulate
the conduction properties of the junction. Depending on the electronic coupling,
Γ, between the molecule and the gold electrodes, different transport regimes can
be distinguished. We show measurements on junctions incorporating different
single-molecule systems which demonstrate the distinction between these
regimes, as well as the experimental limitations in controlling the exact value
of Γ.
We consider a quantum dot with ${\cal K}{\geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.
In a single state of a quantum dot the Kondo effect arises due to the
spin-degeneracy, which is present if the dot is occupied with one
electron (N=1) . The eigenstates of a carbon nanotube quantum dot
possess an additional orbital degeneracy leading to a fourfold shell
pattern. This additional degeneracy increases the possibility for the
Kondo effect to appear. We revisit the Kondo problem in metallic carbon
nanotubes by linear and nonlinear transport measurement in this regime,
in which the fourfold pattern is present. We have analyzed the ground
state of CNTs, which were grown by chemical vapor deposition, at filling
N=1,N=2 , and N=3 . Of particular interest is the half-filled shell,
i.e., N=2 . In this case, the ground state is either a paired electron
state or a state for which the singlet and triplet states are
effectively degenerate, allowing in the latter case for the appearance
of the Kondo effect. We deduce numbers for the effective missmatch
δ of the levels from perfect degeneracy and the exchange energy J
. While δ˜0.1-0.2 (in units of level spacing) is in
agreement with previous work, the exchange term is found to be
surprisingly small: J≲0.02 . In addition we report on the
observation of gaps, which in one case is seen at N=3 and in another
is present over an extended sequence of levels.
We review mechanisms of low-temperature electronic transport through a quantum dot weakly coupled to two conducting leads. Transport in this case is dominated by electron-electron interaction. At temperatures moderately lower than the charging energy of the dot, the linear conductance is suppressed by the Coulomb blockade. Upon further lowering of the temperature, however, the conductance may start to increase again due to the Kondo effect. We concentrate on lateral quantum dot systems and discuss the conductance in a broad temperature range, which includes the Kondo regime.
Coherent electronic transport through a double quantum dot (2qd) system connected in a series with electrodes is studied by means of nonequilibrium Green functions and using the equation of motion method, in which all electron correlations in the 2qd are treated exactly. For moderate Coulomb interactions we predict features in a conductance characteristics resulting from transmission through triplet states, which can be strongly activated for larger source-drain voltages. The analysis of the spin-spin correlation functions shows strong antiferromagnetic correlations arising from transport through the singlet state and a reduction of the total magnetic moment. However, when the transmission channel corresponding to the triplet state becomes activated the antiferromagnetic correlations are much weaker, the spins behave as free electrons spins and strongly fluctuate. We speculate that this effect can be seen in wide range of a gate voltage for a double electron occupancy of the 2qd.
The magnetic character of the ground state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is found that the coupling to the continuum of propagating states on the leads, in conjunction with the electron-electron interactions, may result in a delocalization of the bound state of the two electrons. This, in turn, reduces significantly the range of the Coulomb interaction parameters over which singlet-triplet transitions can be realized. It is also found that the coupling to the leads favors the singlet ground state.
We consider an “impurity” with a spin degree of freedom coupled to a finite reservoir of noninteracting electrons, a system which may be realized by either a true impurity in a metallic nanoparticle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong- and the weak-coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite-size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity and the local susceptibilities. Extensive quantum Monte Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir—the “clean Kondo box” model—we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parities and for the canonical and the grand-canonical ensembles.
In a tunnelling experiment across a quantum dot it is possible to change the coupling between the dot and the contacts at will, by properly tuning the transparency of the barriers and the temperature. Gate voltages allow for changes of the relative position of the dot addition energies and the Fermi level of the leads. Here we discuss the two limiting cases: weak and strong coupling in the tunnelling Hamiltonian. In the latter case Kondo resonant conductance can emerge at low temperature in a Coulomb blockade valley. We give a pedagogical approach to the single-channel Kondo physics at equilibrium and review theNozì eres scattering picture of the correlated fixed point. We emphasize the effect of an applied magnetic field and show how an orbital Kondo effect can take place in vertical quantum dots tuned both to an even and to an odd number of electrons at a level crossing. We extend the approach to the two-channel overscreened Kondo case and discuss recent proposals for detecting the non-Fermi liquid fixed point which could be reached at strong coupling.
A problem of electronic correlations is considered for two specific mesoscopic systems: the quantum point contact (QPC) and the double quantum dot (2QD) system. The systems are described using a generalized Anderson Hamiltonian. We show that charge fluctuations are relevant for electronic transport. In the QPC a local accumulation of charge and the dynamical Coulomb blockade effect lead to the 0.7 structure in the conductance characteristics. The evolution of the conductance with a magnetic field and in non-equilibrium situations is presented as well. The double quantum dot is studied in the approach, in which correlations within the 2QD are treated exactly, whereas the coupling of the 2QD to the leads is considered in the approximation valid at temperatures above the Kondo temperature. We analyse the evolution of the gate voltage dependence of the spin correlation functions and the conductance with the change of the interdot hopping. For the hopping parameter greater than a threshold value of the on-dot repulsion the physics of the device is dominated by the ground state eigenstates of the 2QD and antiferromagnetic correlations in the case of the doubly occupied 2QD. With a decrease of the interdot hopping repulsion below the threshold we observe a significant reduction of the antiferromagnetic coupling between the dots together with an enhanced occupation of the triplet states.
