Electronic transport through a quantum wire with a side-coupled quantum dot

Abstract

We describe the Kondo resonance in quantum dots employing the atomic model. We calculate approximate Green's functions of the impurity Anderson model employing the exact solution of the system with a conduction band with zero width, and we use the completeness condition to choose the position of that band. At low temperatures, there are two solutions close to the chemical potential µ, satisfying this condition, and we choose the one with minimum Helmholtz free energy, considering that this corresponds to the Kondo solution. At high temperatures, this solution no longer exist, corresponding to the disappearance of the Kondo peak. We present curves of density of states that characterize the Kondo peak structure problem. As a simple application we calculate the conductance of a side-coupled quantum dot and we obtain good agreement with recent experimental results.Keywords: Electronic transport; Side-coupled quantum dot; Kondo resonance I. CONDUCTANCE OF A SIDE-COUPLED QUANTUM DOTThe Kondo effect explains the increased resistivity shown by a metal with magnetic impurities at low temperatures. The Kondo effect in quantum dots has been theoretically predicted since 1988 [1], and recent experiments confirmed its presence [2]. These systems can be modelled by the Anderson impurity model, and in this paper we apply the impurity atomic model to study the electronic transport through a quantum wire with a side-coupled quantum dot (QD). This system has been studied, from the theoretical point of view, [3,4] and has been recently studied experimentally [5,6].In Fig. 1 we present a pictorial view of a simple onedimensional quantum wire with a side-coupled Anderson impurity with infinite Coulomb repulsion U at site 0. The Hamiltonian of the system can be written aswhere the first term represents the noninteracting wire, characterized by free conduction electrons (c-electrons), the second describes the QD described by a localized f level E f ,σ , (we employ the f letter to indicate localized electrons at the impurity site) and the last one corresponds to the tunneling, where the hybridization V denotes the tunneling matrix element between the QD level and the site 0 of the quantum wire, and for simplicity we consider a constant hybridization V . We employ the Hubbard operators [7,8] to project out the double occupation state | f , 2 , from the local states on the impurity. As the X Hubbard operators do not satisfy the usual fermion commutation relations, the diagrammatic methods based on Wick's theorem are not applicable, and one has to use the product rules

Effect of a Carbon Nanotube on Ballistic Conduction through Single-Quantum-Dot

“…The quantum dot was modeled by the atomic approach [16,15] and the leads at the points (L and R) were represented by two square bands where the Green's function can written as n the last few decades, low-dimension systems have been the focus of great interest on the part of the scientific community [1]. Due to their extraordinary physical properties, these carbon-based systems have applications in areas ranging from medicine: such as DNA nanosensors [2], to nanoelectronics: with quantum dot systems interacting with graphene [3] and carbon nanotubes [4].…”

“…( 15). Finally, the approximate GF of the quantum dot connected to leads L and R is written as (16) where is the GF of the leads and must be integrated in the range from -D to D, which is the width of the conduction band. With the atomic approach, the different energies of the c-electrons, which should contribute to the propagators of the effective cumulant , are now replaced by the contribution of a single energy value in .…”

Effect of carbon nanotube on ballistic conduction through single-quantum-dot

“…The quantum dot was modeled by the atomic approach [16,15] and the leads at the points (L and R) were represented by two square bands where the Green Function can written as…”

Kondo effect in a quantum dot—the atomic approach

“…We can say that although the method is not adequate to study the details of the strong coupling between localized and conduction electrons, the atomic approach produces excellent results for dynamical properties like the conductance. Due to its simplicity and low computational cost when compared to numerically reliable methods, like the NRG, DMFT or DMRG, the method is a good choice, when compared to other qualitative methods like the EOM discussed earlier, to study dynamical properties of nanoscopic correlated electron systems like quantum dots [4] and carbon nanotubes [5]. As an example of the usefulness of the method, we use it in the next section to calculate the conductance of a quantum dot sidecoupled to a quantum wire.…”

“…These systems can be modelled by the Anderson impurity model (AIM), and the main objective of this paper is to present the 'atomic approach' as an alternative to study nanoscopic systems that exhibit the Kondo effect. Due to the simplicity of its implementation (practically all the method is analytical) and very low computational cost (a density of states curve can be obtained in a few seconds or less), the atomic approach is a good candidate to describe strongly correlated impurity systems that exhibit the Kondo effect, like quantum dots [4] or carbon nanotubes [5]. The results obtained for both the localized density of states at the chemical potential and dynamical properties (like the conductance) agree very well with those obtained by the numerical renormalization group formalism [6] and by the slave boson mean field approximation [7,8] respectively.…”