g-tensor evaluation in self-assembled quantum dots

In solid state, the first term to be considered in the effective spin Hamiltonian is that representing the electronic Zeeman interaction. In a doublet state with $S=1/2$, the two levels will diverge linearly with the magnetic field ($B$), with slopes $\pm 1/2g\beta B$. In practice, the Zeeman interaction not depends only on the angle between the effective spin vector (\overrightarrow {S}) and $\overrightarrow{B}$ but depends also on the angle that $\overrightarrow{B}$ makes with certain axes defined by the sample symmetry. Taking into account this kind of anisotropy, the effective spin Hamiltonian is $\beta(\overrightarrow{B}\cdot\makebox[0.1cm][l]{\raisebox{1ex} {$\leftrightarrow$}} g\cdot\overrightarrow{S}$), where $\makebox[0.1cm][l]{\raisebox{1ex}{$\leftrightarrow$}}g $ is the g-tensor. Since electrons can be individually trapped into quantum dots (QDs) in a controllable manner, they may represent a good candidate for the successfully implementation of spintronics into semiconductor heterostructures. In this work we realized magneto-capacitance spectroscopy (CV) in order to obtain the localization energies and the evolution of the Zeeman splitting for the s and p electron confined levels in InAs self-assembled quantum dots (SAQDs). The CV experiments were performed at 2K using lock- in amplifiers at a frequency of 7.5KHz. An AC amplitude of 10 mV was superimposed on a varying DC bias ranging from -2 V to 0.5 V with a signal/noise ratio above $10^{4}$. Aligning $\overrightarrow{B}$ with different crystallographic directions, we measured the g-tensor showing the existence of a high anisotropy degree. The g-factor values obtained ranges between 1.9 and 0.7, with $\overrightarrow{B}\parallel001$ and $\overrightarrow{B}\parallel110$ respectively.