Gate control of a quantum dot single-electron spin through Geometric Phases: Feynman Dis-entangling Method

Among recent proposals for next-generation, non-charge-based logic is the notion that a single electron can be trapped and its spin can be manipulated by moving the quantum dot adiabatically in a closed loop (Berry effect) through the application of gate potentials. In this paper, we present numerical simulations and analytical expressions of such spins in single electron devices for a quantum dot. Using analytical and numerical techniques, we show that spin orbit coupling in III-V type semiconductor will enhance the transition probability of the electron spin over pure Rashba and or pure Dresselhaus cases. With the help of Feynman Dis-entangling technique of the non-abelean operator, we found the exact analytical expression for the propagator of an electron moving under the influence of three different cases: pure Rashba, pure Dresselhaus and equal strength of Rashba and Dresselhaus spin orbit coupling. For the most general cases where the solution of the propagator becomes non-trivial, we carry out the numerical simulations of such propagator.