Electron Localization, Tunneling and Energy Spectrum for Systems of Double Quantum Dots
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Electron Localization, Tunneling and Energy Spectrum for Systems of Double Quantum Dots Igor Filikhin, Sergei Matinyan and Branislav Vlahovic Department of Physics, North Carolina Central University, 1801 Fayetteville Street, Durham, NC 27707, USA ABSTRACT Semiconductor heterostructures as quantum dots demonstrate discrete atom-like energy level structure based on several hundred of electron confinement states. In the case of double QD (DQD) or double QR (DQR), there is a single electron spectrum composed of a set of quasidoublets. We study these specific spectrum properties with their relation to the electron tunneling in DQD (DCQR) when the wave function of electron localized initially in one of the double quantum object is spread into whole system. The double InAs/GaAs quantum dots are considered within the effective approach. Tunneling in DQD is studied in connection with change of interdot distance and QD geometry. There are two types of such tunneling in DQD. The first is related to tunneling in the system of two identical QDs; the second one occurs in the system of non-identical QDs. The tunneling in the DQR is a tunneling in the system with non-identical quantum objects. The quasi-doublets of the DQD spectrum play an important role in the tunneling. We study effect of violation of symmetry of DQD geometry on the tunneling and show that the violation of symmetry makes difficulties for such tunneling. INTRODUCTION Tunneling and Chaos are inalienable phenomena in the meso- and nano world. Technology itself with its imperfection of shapes of quantum dots (QDs) and quantum rings (QRs) provides the chaotic behavior in the QD and QR [1] what has a strong influence on their transport and other properties. The problem of quantum chaos in these objects has a relatively long history, just since they entered science and technology [2-6] (for recent review see [7]). One of the main results of these studies, sometime based on the semi classical approach, is that their chaotic phenomena sensitively depend on geometry and, first of all, on the symmetry of these objects. The second fundamental phenomenon characterizing the behavior of these confined objects is a tunneling expressing the matter wave structure of quantum mechanics. The tunneling is well known from textbooks and best discussed by an example of the barrier penetration in a double well potential. However, in the general sense, as applied to the confined nano-objects, tunneling is a dynamical by nature, not a direct result of the existing the energetic barrier, it is the property of the wave function of the whole system. The main feature of this so called dynamical tunneling is well known from energetic barrier examples splitting of the degenerate pairs of level when the coupling between objects due to their common wave function resulting the forming two nearly degenerate eigenstates which are the linear combinations of the wave functions of the isolated objects.
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In the present paper we consider the real situation, and this is one of the goals of the presen
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