Kondo effects in quantum dots systems

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

Screened spin−1 and −1/2 Kondo effect in a triangular quantum dot system with interdot Coulomb repulsion

The modeling and comparative analysis of the relaxation processes in four different heterostructures: traditional heterotransistor, heterotransistor with two channels (heterojunctions), heterotransistor with two channels and a system of quantum dots (QDs), as well as heterotransistor with two channels and two systems of quantum dots were made. It is shown that the heating of electrons in high electric fields in heterotransistors with embedded quantum dots with two heterojunctions is less intensive, and the values of the drift velocity is higher than in the other structures under study.

We investigate the effects of spin-polarized leads on the Kondo physics of a quantum dot using the numerical renormalization group method. Our study demonstrates in an unambiguous way that the Kondo effect is not necessarily suppressed by the lead polarization: While the Kondo effect is quenched for the asymmetric Anderson model, it survives even for finite polarizations in the regime where charge fluctuations are negligible. We propose the linear tunneling magnetoresistance as an experimental signature of these behaviors. We also report on the influence of spin-flip processes.

Though electron spins in electrically defined silicon (Si) quantum dot systems have been extensively employed for physical realization of quantum processing units, their application to quantum sensing has not been active compared to the case of photonic qubits and nitrogen-vacancy spins in diamonds. This work presents a comprehensive study on the feasibility of Si quantum dot structures as a physical platform for implementation of a sensing protocol for magnetic fields. To examine sensing operations at a systematic level, we adopt in-house device simulations taking a Si double quantum dot (DQD) system as a target device where the confinement of electron spins is controlled with electrical biases in a Si/Si-germanium heterostructure. Simulation results demonstrate the fairly nice utility of the Si DQD platform for detecting externally presented static magnetic fields, and, more notably, reveal that sensing operations are not quite vulnerable to charge noise that is omnipresent in solid materials. As a rare study that presents in-depth discussion on operations of quantum sensing units at a device-level based on computational modeling, this work can deliver practical insights for potential designs of sensing units with electron spins in Si devices.

The nondestructive observation of correlation between optical characteristic and morphologic feature within capped ZnCdSe/ZnSe quantum dots system

Strong correlation behaviors play a pivotal role in realizing novel, high-performance, low-power nanoscale electronic devices. In this study, we theoretically design a molecular switch based on a metal-free polycyclic aromatic hydrocarbon diradical molecule dominated by strong electron-electron repulsions. By establishing a customized simulation framework that combines density functional theory with the numerical renormalization group method, and with the aid of a side-coupled two-orbital Anderson model, we systematically simulate the quantum transport governed by various kinds of Kondo effects. When the central energy level sweeps upward, the linear conductance tends to reach its unitary limit in the low-temperature regime, driven by the broadening two-stage Kondo effect window. As the side energy increases, a quantum phase transition from the two-stage Kondo effect to the spin-1/2 Kondo effect emerges, resulting in a stable, full conductance plateau. Furthermore, by tuning the exchange coupling between the central and the side orbitals, we simulate the impact of precisely adjusting the intramolecular dihedral angle of the molecule on the transport properties. The linear conductance exhibits a transition from zero to the unitary limit as the molecule smoothly evolves from the antiferromagnetic to the ferromagnetic regime. These findings provide valuable insights into the dynamical and thermodynamical properties of complex polycyclic aromatic hydrocarbon systems. Our suggested "abinitio + model calculation" theoretical framework may offer a promising methodology for exploring the complex Kondo physics in real magnetic nanosystems.

We discuss the Kondo effect in an electron system dynamically coupled with local Jahn-Teller phonons. For the purpose, we consider the two-orbital Anderson model including both Coulomb interactions and the coupling between electrons and Jahn-Teller phonons on an impurity site. Note that in this paper, we consider a quarter-filling case. First we analyze a local problem and confirm a spin-vibronic quartet ground state, characterized by the direct product of spin and vibronic degrees of freedom. Next we include the hybridization term and analyze the model by using a numerical renormalization group method. From the evaluation of entropy, specific heat, and several kinds of susceptibilities, it is found that spin and total angular momenta are simultaneously screened by conduction electrons, leading to the Kondo phenomenon due to the entropy release of ln 4 of the local spin-vibronic state. A possibility of heavy-electron formation in the spin-vibronic Kondo effect is briefly discussed.

We investigate the Josephson effect through a two-level quantum dot with an exchange coupling between two dot electrons. We compute the superconducting phase relationship and construct the phase diagram in the superconducting gap--exchange coupling plane in the regime of the singlet-triplet transition driven by the exchange coupling. In our study two configurations for the dot-lead coupling are considered: one where effectively only one channel couples to the dot, and the other where the two dot orbitals have opposite parities. Perturbative analysis in the weak-coupling limit reveals that the system experiences transitions from 0 to $\pi$ (negative critical current) behavior, depending on the parity of the orbitals and the spin correlation between dot electrons. The strong coupling regime is tackled with the numerical renormalization group method, which first characterizes the Kondo correlations due to the dot-lead coupling and the exchange coupling in the absence of superconductivity. In the presence of superconductivity, many-body correlations such as two-stage Kondo effect compete with the superconductivity and the comparison between the gap and the relevant Kondo temperature scales allows to predict a rich variety of phase diagrams for the ground state of the system and for the Josephson current. Numerical calculations predicts that our system can exhibit Kondo-driven 0-$\pi$-0 or $\pi$-0-$\pi$ double transitions and, more interestingly, that if proper conditions are met a Kondo-assisted $\pi$-junction can arise, which is contrary to a common belief that the Kondo effect opens a resonant level and makes the 0-junction. Our predictions could be probed experimentally for a buckminster fullerene sandwiched between two superconductors.

We discuss the effect of quantum interference on transport through a quantum dot (QD) system. We introduce an indirect coherent coupling parameter α, which provides constructive/destructive interference in the transport current depending on its phase and the magnetic flux. We estimate the current through the QD system using the non-equilibrium Green's function method as well as the Bloch equation method under a large bias voltage condition. The visibility of the Aharonov–Bohm oscillation is evaluated. For a large inter-dot Coulomb interaction, the current is strongly suppressed by the quantum interference effect, while the current is restored by applying an oscillating resonance field with the frequency of twice the inter-dot tunnelling energy.

Polarization and excitation power-dependent photoluminescence of magnetic/non-magnetic coupled quantum dots

The effect of a magnetic field on the spectral density of a S = 1/2 Kondo impurity is investigated at zero and finite temperatures by using Wilson's numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value H(c)(T = 0) approximately 0.5T(K), where T(K) is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on CexLa1-xAl2,x = 0.0063. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states, this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect---the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiments, due to the complex interplay between Dirac, van Hove, and Kondo physics.

Semiconductor quantum dots are usually compared to artificial atoms, because their electronic structure consists of discrete energy levels as for natural atoms. These artificial systems are integrated in solid materials and can be localized with a spatial precision of the order of nanometers. Besides, they conserve their quantum properties even at quite high temperatures (∼ 10 K). These properties make quantum dots one of the most suitable systems for the realization of quantum devices and computers. However, the energy states and the optical properties of quantum dots are much more complicated than for atoms, because a quantum dot is never an isolated potential well. Instead, its electronic structure depends on the crystallin structure of the semiconductor material and on the Coulomb ion-electron and electron-electron correlations. In particular, the presence of several valence bands and their mixing, induced by quantum confinement, gives rise to novel properties which are still not completely understood and exploited in applications. To get a major advance in this field, a full deterministic control of the spatial shape of the quantum confinement is needed, combined with a deeper understanding of the connections between electronic and optical properties. This thesis work has these two main objectives. We realized and experimentally studied different quantum dot systems, in pyramidal hetero-structures grown with MOCVD techniques. These systems allowed the realization of several different geometries for the carrier confining potential, with a precision in the order of nanometers. The optical characterization has been obtained in particular by means of polarization-resolved microphotoluminescence, magneto-photoluminescence, excitation photoluminescence (PLE), and interferometry techniques. For single quantum dots, we have observed and characterized for the first time new excitonic complexes, arising from excited hole states. This allowed a full caracterizatioon of the valence band hole states in our peculiar system. By means of photon correlation measurements, we have also experimentally demonstrated that, even in presence of a large family of exciton states, these quantum dot systems can emit single photons. We have then realized much more complex quantum dot structures, double dot systems (quantum dot molecules) and a completely new system called Dot-in-Dot (DiD). This latter is composed by a small inner dot surrounded by an electrostatic potential well (which can be considered as an outer elongated dot). Such a composite system is characterized by a strong valence band mixing. This state superposition is however very sensitive to small variations of the confining potential. Therefore the degree of valence band mixing can be easily switched by the introduction of a week external field. Since the valence band mixing determines the polarization properties of the emitted light, the DiD changes the polarization properties of its emission spectrum under the action of an external field. In particular, we have experimentally demonstrated this effect for an external static magnetic field, while we have numerically predicted a very similar effect for a static electric field. In the latter case, the polarization switching is a direct consequence of the quantum confined Stark effect induced in the DiD. Hence the DiD appears to be an ideal candidate for realizing emitters of single photons with tunable and controllable polarization.

Quantum dot systems have shown numerous applications in random lasing and light localization phenomena. Conventional simulations of radiation in quantum dot systems rely heavily on a differential formulation of Maxwell's equations to compute dynamics. Unfortunately, the computational costs incurred by the underlying differencing mechanism inherent in such models renders them infeasible for simulations in three dimensions. We propose an integral-equation framework to self-consistently describe the dynamics of a disordered system of quantum dots driven by an incident laser pulse. By adopting an integral formulation of Maxwell's equations, we remove the “radiation grid” in favor of highly optimized point-to-point communication of fields through integral equations. By adopting a semiclassical approximation of the quantum dot system, we partition the computational problem into two distinct parts: (1) determination of source polarizations through evolution of the optical Bloch equations, and (2) evaluation of radiation patterns with electric field integral equation techniques. The solution of each part proceeds explicitly in time, facilitating a complete description of both quantum dots and electromagnetic fields at each timestep, giving rise to phenomena such as localization, photon echo effects, and nonlinear response patterns.