IntroductionAdvances in modern high precision methods of nanostructures growth such as molecular beam epitaxy, laser deposition, StranskiKrastanov mode, and metalorganic chemical vapor deposition, provide ample opportunities for production of not only the isolated QDs but also two or more closely spaced coupled QDs − quantum dot molecules (QDMs). Whereas QDs are artificial atoms, the QDMs are artificial molecules with bonding and anti-bonding orbitals [1]. From the practical point of view, an interesting coupling between QDs provides wide possibilities for QDMs applications in modern opto-and nanoelectronics. In contrast to atoms in molecules, the charge carriers' confinement in each QD and the coupling between QDs in a QDM can be controlled separately. Redistribution of the energy spectrum and wave functions (WFs) in the QDM leads to dramatic changes in the optical and transport properties of QDMs compared to single QDs [2]. In real growth conditions, the obtained symmetric QDMs are rather rare; more often, due to various physical and technical reasons, grown lateral QDMs are asymmetric [3][4][5]. Similarities between the energy spectra of symmetric molecules (e.g., O 2 , H 2 , or N 2 ) and symmetric QDMs, and, correspondingly, asymmetric molecules (e.g., CO, CO 2 , or NO 2 ) and asymmetric QDMs potentially allow one to design various biochemical sensors and detectors with a single molecule sensitivity [6,7]. For applications in semiconductor based photonic devices [8,9] one needs to find the energy spectrum of charge carriers as well as the possible optical transitions in QDMs considering quantum confinement effects. Electronic and optical properties of QDMs largely depend on the shape and sizes of the QDs and the confining potential [10][11][12][13][14]. Significant differences in size and chemical composition of composite QDs complicate the theoretical description of the QDM properties. Obviously, the charge carrier is more likely to be localized in a large QD, yet the presence of one or more small satellites changes the charge carrier behavior fundamentally due to the rearrangement of energy levels in a large QD. This complex problem can be described analytically with the correct choice of the equation for the entire QDM surface [15]. Theoretical study of semiconductor QDMs allows reducing the number of expensive experiments to design the optimal structure of new generation photonic devices. In this paper, the electronic states and direct interband absorption of light are theoretically investigated in the asymmetric QDM having Cassini lemniscate shaped surface and the isthmus connecting two QDs (Figure 1).
Electronic StatesLet us consider an impermeable asymmetric QDM consisting of two QDs schematically shown on Figure 1. The surface equation of the QDM in cylindrical coordinates and the charge carrier (an electron or hole) potential energy in the QDM are as follows: where c 1 and c 2 are the focal length of the small and large semi-lemniscates respectively, a 1 and a 2 are the product of distances from foc...
