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We consider the transport and the noise characteristics for the case of a T-shape double quantum dot system using the equation of motion method. Our theoretical results, obtained in an approximation equivalent to the Hartree-Fock approximation, account for non-zero on-site Coulomb interaction in both the detector and side dots. The existence of a non-zero Coulomb interaction implies an additional two resonances in the detectors dot density of states and thereafter affects the electronic transport properties of the system. The systems conductance presents two Fano dips as function of the energy of the localized electronic level in the side dot. The Fano dips in the systems conductance can be observed both for strong (fast detector) and weak coupling (slow detector) between the detector dot and the external electrodes. Due to stronger electronic correlations the noise characteristics in the case of a slow detector are much higher. This setup may be of interest for the practical realization of qubit states in quantum dots systems.
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We investigate the thermoelectric properties of a T-shaped double quantum dot system described by a generalized Anderson Hamiltonian. The systems electrical conduction (G) and the fundamental thermoelectric parameters such as the Seebeck coefficient ($S$) and the thermal conductivity ($kappa$), along with the systems thermoelectric figure of merit (ZT) are numerically estimated based on a Greens function formalism that includes contributions up to the Hartree-Fock level. Our results account for finite onsite Coulomb interaction terms in both component quantum dots and discuss various ways leading to an enhanced thermoelectric figure of merit for the system. We demonstrate that the presence of Fano resonances in the Coulomb blockade regime is responsible for a strong violation of the Wiedemann-Franz law and a considerable enhancement of the systems figure of merit ($ZT$).
We consider the non-equilibrium zero frequency noise generated by a temperature gradient applied on a device composed of two normal leads separated by a quantum dot. We recall the derivation of the scattering theory for non-equilibrium noise for a general situation where both a bias voltage and a temperature gradient can coexist and put it in a historical perspective. We provide a microscopic derivation of zero frequency noise through a quantum dot based on a tight binding Hamiltonian, which constitutes a generalization of the pioneering work of Caroli et al. for the current obtained in the context of the Keldysh formalism. For a single level quantum dot, the obtained transmission coefficient entering the scattering formula for the non-equilibrium noise corresponds to a Breit-Wigner resonance. We compute the delta-$T$ noise as a function of the dot level position, and of the dot level width, in the Breit-Wigner case, for two relevant situations which were considered recently in two separate experiments. In the regime where the two reservoir temperatures are comparable, our gradient expansion shows that the delta-$T$ noise is dominated by its quadratic contribution, and is minimal close to resonance. In the opposite regime where one reservoir is much colder, the gradient expansion fails and we find the noise to be typically linear in temperature before saturating. In both situations, we conclude with a short discussion of the case where both a voltage bias and a temperature gradient are present, in order to address the potential competition with thermoelectric effects.
We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. We show that the master equation in the occupation-state basis includes only the low-order terms with respect to the interdot coupling compared with the more accurate master equation in the eigenstate basis. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.
We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branching current and the noise crossed correlations in terms of single and two-particle Greens function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunneling, the antisymmetric case (the two levels have opposite energies with respect to the superconducting chemical potential) optimizes the Crossed Andreev Reflection (CAR) process while the symmetric case (the two levels have the same energies) favors the Elastic Cotunneling (EC) process. Switching on the direct tunneling tends to suppress the CAR process, leading to negative noise crossed correlations over the whole voltage range for large enough direct tunneling.
We analyze the transport properties of a double quantum dot device with both dots coupled to perfect conducting leads and to a finite chain of N non-interacting sites connecting both of them. The inter-dot chain strongly influences the transport across the system and the Local Density of States of the dots. We study the case of small number of sites, so that Kondo box effects are present, varying the coupling between the dots and the chain. For odd N and small coupling between the inter-dot chain and the dots, a state with two coexisting Kondo regimes develops: the bulk Kondo due to the quantum dots connected to leads and the one produced by the screening of the quantum dots spins by the spin in the finite chain at the Fermi level. As the coupling to the inter-dot chain increases, there is a crossover to a molecular Kondo effect, due to the screening of the molecule (formed by the finite chain and the quantum dots) spin by the leads. For even N the two-Kondo temperatures regime does not develop and the physics is dominated by the usual competition between Kondo and antiferromagnetism between the quantum dots. We finally study how the transport properties are affected as N is increased. For the study we used exact multi-configurational Lanczos calculations and finite U slave-boson mean-field theory at T = 0. The results obtained with both methods describe qualitatively and also quantitatively the same physics.
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