Spin exciton in a quantum dot with spin-orbit coupling at high magnetic field

Coulomb interactions of few (N) electrons confined in a disk-shaped quantum dot, with a large magnetic field ${B=B}^{*}$ applied in the z direction (orthogonal to the dot), produce a fully spin-polarized ground state. We numerically study the splitting of the levels corresponding to the multiplet of total spin $S=N/2\mathrm{}$ (each labeled by a different total angular momentum $J_z)$ in the presence of an electric field parallel to B, coupled to S by a Rashba term. We find that the first excited state is a spin exciton with a reversed spin at the origin. This is reminiscent of the quantum Hall ferromagnet at filling one, which has the skyrmionlike state as its first excited state. The spin-exciton level can be tuned with the electric field and infrared radiation can provide energy and angular momentum to excite it.