In this thesis, possibility of quantum phase transition in systems composed of quantum dots will be studied. We also investigate the consequence of this phase transition on transport. We particularly consider a triple quantum dot system (three quantum dots sitting on the corners of an equilateral triangle) coupled to three leads symmetrically. To probe quantum phase transition we utilize slave-boson mean-field theory and to investigate transport properties we use scattering formalism. We detect a competition between Kondo and non-Kondo regime in this system. This competition affects transport in a way that conductance and noise will become zero when the non-Kondo regime dominates, in other words when the system crosses the phase boundaries. The results of this research can motivate experiments on the same systems to probe quantum phase transition and provides theoretical background for the experiment. It can also motivate future theoretical work using different methods from mean-field theory.
In this thesis, possibility of quantum phase transition in systems composed of quantum dots will be studied. We also investigate the consequence of this phase transition on transport. We particularly consider a triple quantum dot system (three quantum dots sitting on the corners of an equilateral triangle) coupled to three leads symmetrically. To probe quantum phase transition we utilize slave-boson mean-field theory and to investigate transport properties we use scattering formalism. We detect a competition between Kondo and non-Kondo regime in this system. This competition affects transport in a way that conductance and noise will become zero when the non-Kondo regime dominates, in other words when the system crosses the phase boundaries. The results of this research can motivate experiments on the same systems to probe quantum phase transition and provides theoretical background for the experiment. It can also motivate future theoretical work using different methods from mean-field theory.
Semiconductor quantum dot structure provides a promising basis for quantum information processing, within which to reveal the quantum phase and charge transport is one of the most important issues. In this paper, by means of the numerical renormalization group technique, we study the quantum phase transition and the charge transport for a parallel triple dot device in the strongly correlated limit, focusing on the effect of inter-dot hopping t beyond the Kondo regime. We find the quantum behaviors depend closely on the initial electron number on the dots, and the present model may map to single, double, and side-coupled impurity models in different parameter spaces. An orbital spin-1/2 Kondo effect between the conduction leads and the bonding orbital, and several magnetic-frustration phases are demonstrated when t is adjusted to different regimes. To understand these phenomena, a canonical transformation of the energy levels is given, and important physical quantities with respect to increasing t and necessary theoretical discussions are shown.
We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson’s numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model. In the framework of an effective model we also explain smearing of the entanglement transition for cases when the symmetry of the triple quantum dot system is relaxed.
The spectral properties and the quantum phase transitions in parallel triple quantum dot systems are investigated using the numerical renormalization-group method. For small interdot hopping t, the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between the dots is identified in the spectra and is consistent with that obtained by the perturbation theory. With increasing t, due to the competition between the RKKY exchange and the direct exchange between dots, there exist two first-order quantum phase transitions between the phases with the local spin Sdot=3∕2, 1∕2, and 0 on the dots. At low temperature, the local spin Sdot=3∕2 is partially screened to a residual spin S=1, while the local spin Sdot=1∕2 is totally screened. In both local quadruplet and doublet states, the Kondo resonance accompanied with a conductance of the unitary limit 2e2∕h is observed, while no Kondo effect is found in the local spin-singlet state.
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.
Observing quantum phase transitions in mesoscopic systems is a daunting task, thwarted by the difficulty of experimentally varying the magnetic interactions, the typical driving force behind these phase transitions. Here we demonstrate that in realistic coupled double-dot systems, the level energy difference between the two dots, which can be easily tuned experimentally, can drive the system through a phase transition, when its value crosses the difference between the intra- and inter-dot Coulomb repulsion. Using the numerical renormalization group and the semi-analytic slave-boson mean-field theory, we study the nature of this phase transition, and demonstrate, by mapping the Hamiltonian into an even-odd basis, that indeed the competition between the dot level energy difference and the difference in repulsion energies governs the sign and magnitude of the effective magnetic interaction. The observational consequences of this transition are discussed.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime.The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy.We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase.A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy.In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD).While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state.By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs.Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.