Position-dependent dynamics of electronic spin-subband entanglement in a Rashba nanoloop

In this paper, as a complementation to our previous reports, we study the position dependency of the electronic spin-subband entanglement for different spin initial conditions in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We compute the von Neumann entropy, a measure of entanglement, as a function of time by explicitly including the confining potential and the Rashba spin-orbit (SO) coupling into the Hamiltonian. An analysis of the von Neumann entropy demonstrates that, due to a fictitious magnetic field arising from Rashba SO coupling, the spin-subband entanglement strongly depends upon the location of electron within the loop. Moreover, it is shown that the position dependency of entanglement dynamics depends upon the spin initial state. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with just one local minimum in each oscillation. On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates either with two local minima in each oscillation at θ ≠ 0, π or without local minima at θ = 0, π. The physical reasons behind such behavior are also discussed.