Generalized description of few-electron quantum dots at zero and nonzero magnetic fields

We introduce a generalized ground state variational wavefunction for parabolically confined two-dimensional quantum dots that equally applies to both cases of weak (or zero) and strong magnetic field. The wavefunction has a Laughlin-like form in the limit of infinite magnetic field, but transforms into a Jastrow–Slater wavefunction at zero magnetic field. At intermediate magnetic fields (where a fraction of electrons is spin-reversed) it resembles Halperin’s spin-reversed wavefunction for the fractional quantum Hall effect. The properties of this variational wavefunction are illustrated for the case of two-dimensional quantum dot helium (a system of two interacting electrons in a parabolic confinement potential) where we find the description to be an excellent representation of the true ground state for the whole range of magnetic fields. Quantum dots are fabricated semiconductor nanostructures in which charge carriers, such as electrons, are confined in a small region of space [1–8], usually in two dimensions (2D). In particular, the case of few-electron quantum dots subject to a perpendicular magnetic field is of great interest, because, under all experimental conditions, single-electron confinement energy, cyclotron energy and the strength of electronic correlations are of the same order of magnitude, producing very rich physics. The application of a perpendicular magnetic field to a quantum dot plays a fundamental role in changing the nature of single-electron levels from those for the 2D harmonic oscillator to Landau levels in which electronic correlations are strongly enhanced, resulting in behaviour as seen in the fractional quantum Hall effect (FQHE) regime [9–12]. The Hamiltonian for a 2D quantum dot system consisting of N electrons confined by a parabolic potential and subject to a magnetic field, Bz, perpendicular to the dot plane is written as: