  In this paper, a detailed analysis of anisotropic effects on the phonon
induced spin relaxation rate in III-V semiconductor quantum dots (QDs) is
carried out. We show that the accidental degeneracy due to level crossing
between the first and second excited states of opposite electron spin states in
both isotropic and anisotropic QDs can be manipulated with the application of
externally applied gate potentials. In particular, anisotropic gate potentials
enhance the phonon mediated spin-flip rate and reduce the cusp-like structure
to lower magnetic fields, in addition to the lower QDs radii in III-V
semiconductor QDs. In InAs QDs, only the Rashba spin-orbit coupling contributes
to the phonon induced spin relaxation rate. However, for GaAs QDs, the Rashba
spin-orbit coupling has a contribution near the accidental degeneracy point and
the Dresselhaus spin-orbit coupling has a contribution below and above the
accidental degeneracy point in the manipulation of phonon induced spin
relaxation rates in QDs.
