  Berry phase in semiconductor quantum dots (QDs) can be induced by moving the
dots adiabatically in a closed loop with the application of the distortion
potential in the lateral direction. We show that the Berry phase is highly
sensitive to the electric fields arising from the interplay between the Rashba
and the Dresselhaus spin-orbit couplings. We report that the accumulated Berry
phase can be induced from other available quantum state that are only differed
by one quantum number of the same spin state. The sign change in the g-factor
due to the penetration of the Bloch wavefunctions into the barrier material can
be reflected in the Berry phase. We solve the time dependent
Schr$\mathrm{\ddot{o}}$dinger equation and investigate the evolution of the
spin dynamics during the adiabatic movement of the QDs in the 2D plane. Our
results might open the possibilities of building a topological quantum dot
quantum computer where the Berry phase can be engineered and can be manipulated
with the application of the spin-orbit couplings through gate controlled
electric fields.
