Double-donor complex in vertically coupled quantum dots in a threading magnetic field
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NANO EXPRESS
Open Access
Double-donor complex in vertically coupled quantum dots in a threading magnetic field Ramón Manjarres-García1, Gene Elizabeth Escorcia-Salas1, Javier Manjarres-Torres1, Ilia D Mikhailov2 and José Sierra-Ortega1*
Abstract We consider a model of hydrogen-like artificial molecule formed by two vertically coupled quantum dots in the shape of axially symmetrical thin layers with on-axis single donor impurity in each of them and with the magnetic field directed along the symmetry axis. We present numerical results for energies of some low-lying levels as functions of the magnetic field applied along the symmetry axis for different quantum dot heights, radii, and separations between them. The evolution of the Aharonov-Bohm oscillations of the energy levels with the increase of the separation between dots is analyzed. Keywords: Quantum dots, Adiabatic approximation, Artificial molecule PACS: 78.67.-n, 78.67.Hc, 73.21.-b
Background An important feature in low-dimensional systems is the electron-electron interaction because it plays a crucial role in understanding the electrical transport properties of quantum dots (QDs) at low temperatures [1]. Such systems may involve small or large numbers of electrons as well as being confined in one or more dimensions. The number of electrons in a QD can be varied over a considerable range. It is possible to control the size and the number of electrons and to observe their spatial distributions in QDs. Energy spectrum of two-electron QD with a parabolic confinement, for which two-particle wave equation can be separated completely, has been analyzed previously by using different methods [2-5]. In the present work, we propose another exactly solvable two-electron heterostructure in which two separated electrons are confined in vertically coupled QDs with a special lens-like morphology. Together with two on-axis donors, these two electrons generate an artificial hydrogen-like molecule whose properties can be controlled by varying the geometric parameters and the * Correspondence: [email protected] 1 Group of Investigation in Condensed Matter Theory, Universidad del Magdalena, Santa Marta, Colombia Full list of author information is available at the end of the article
strength of the magnetic field applied along the symmetry axis.
Methods The model which we analyze below consists of two identical, axially symmetrical and vertically coupled QDs with the on-axis donor located in each one of them (see Figure 1). The dimension of the heterostructure is defined by the QDs' radii R, height W, and the separation d between them along the z-axis. We assume that the QDs have a shape of very thin layers whose profiles are given by the following dependence of the thickness of the layers w on the distance ρ from the axis: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wðρÞ ¼ W = 1 þ ðρ=RÞ2 ð1Þ Besides, for the sake of simplicity, we consider a model with infinite barrier confinement, which is defined in cylindrical coordinates as V ðrÞ ¼ 0 if 0 < z < wðρÞ , and V ðrÞ ¼ 1 otherwise. Given th
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