Electronic spectrum of two coupled semiconductor quantum disks under external fields

In the latest years, a great effort has been dedicated to the fabrication and experimental analysis of coupled quantum dots arrays[1,2]. From the applications point of view, this nanosystems have a great potential to be used in quantum dot lasers and memory devices. The simplest system to study is a single pair of coupled quantum dots forming a molecule. It is clear that this system is of fundamental importance to understand the role of the quantum coupling on the electronic properties of nanostructures. In this work, we report calculations of the electronic spectrum and eigenstates of a molecule formed by a single pair of coupled quantum dots. The results are obtained from a one-particle model, within the effective-mass approximation, by assuming a parabolic dispersion relation for electrons. We also study the spectrum in the presence of an external magnetic field, which is oriented normal to the molecule plane. We include the field in the Hamiltonian by a magnetic vector potential by adopting the symmetric gauge. Quantum dots are modeled by a parabolic lateral-confining potential, centered on the axis of each quantum dot and truncated in the bisector plane. The energy spectrum and corresponding eigenstates for a single quantum dot can be obtained analytically. We use these solutions to construct the corresponding solutions for the molecule of quantum dots. We study the symmetry properties of the effective Hamiltonian of the system, and we use group theory to establish the appropiated combinations of single quantum dot functions to construct the basis functions of each irreducible representation of the group. We present results for energy spectrum of the quantum-dot molecule as a function of the strength of the coupling and lateral confinement of the dots.