Calculation of Landégfactors for III-V nanowhisker quantum dots and comparison with experiment

Abstract

The coupling between a magnetic field and the spin of an electron confined to a quantum dot is determined by the $g$ factor, which is strongly affected by the structure of the dot. Uncertainties in a dot's geometry and composition can obscure quantitative comparison of theory and experiment. Nanowhisker quantum dots (NWQDs) provide a well-controlled structure that is ideal for such comparison. We have performed detailed three-dimensional numerical calculations of the electronic properties of NWQDs consisting of an $\mathrm{In}\mathrm{P}∕\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ quantum well embedded in a [111] oriented InAs nanowhisker. We have computed $g$ factors, confinement energies, and wave functions for valence and conduction states as a function of dot size. The calculations are in excellent agreement with experiments and differ markedly from $g$ factors obtained from extrapolation of bulk formulas, providing strong confirmation of the effect of angular momentum quenching. The closeness of our results to experiment enables us to identify critical well and barrier widths yielding $g\ensuremath{\approx}0$, which are important for technological applications. We also predict larger and more negative $g$ factors for $\stackrel{P\vec}{B}$ oriented along [111]. The calculations were carried out using eight-band strain-dependent $k∙p$ theory in the envelope-function approximation using a finite difference technique on a real-space grid.