Spin Exciton in quantum dot with spin orbit coupling in high magnetic field

Coulomb interactions of few ($N$) electrons confined in a disk shaped quantum dot, with a large magnetic field $B=B^{\ast }$ 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 $S=N\mathrm{/}2$ (each labeled by a different total angular momentum $J_z$) in 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 skyrmion-like 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.