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We study the variation in the Land$\acute{\text{e}}$ g-factor of electronspins induced by both anisotropic gate potentials and magnetic fields in InAsquantum dots for possible implementation towards solid state quantum computing.In this paper, we present analytical expressions and numerical simulations ofthe variation in the Land$\acute{\text{e}}$ g-factor for both isotropic andanisotropic quantum dots. Using both analytical techniques and numericalsimulations, we show that the Rashba spin-orbit coupling has a majorcontribution in the variation of the g-factor with electric fields before theregime, where level crossing or anticrossing occurs. In particular, theelectric field tunability is shown to cover a wide range of g-factor throughstrong Rashba spin-orbit interaction. Another major result of this paper isthat the anisotropic gate potential gives quenching effect in the orbitalangular momentum that reduces the variation in the E-field and B-fieldtunability of the g-factor if the area of the symmetric and asymmetric quantumdots is held constant. We identify level crossings and anticrossings of theelectron states in the variation of the Land$\acute{\text{e}}$ g-factor. Wemodel the wavefunctions of electron spins and estimate the size of theanticrossing for the spin states $|0,-1,+1/2>$ and $|0,0,-1/2>$ correspondingto a quantum dot that has been recently studied experimentally (Phys. Rev.Lett. \textbf{104}, 246801 (2010)).

physical review. b, condensed matter and materials physics

Manipulation of the Land$\acute{\text{e}}$ g-factor in InAs quantum dots  through the application of anisotropic gate potentials: Exact  diagonalization, numerical and perturbation methods