Orbital ferromagnetism in interacting few-electron dots with strong spin-orbit coupling

We study the ground state of $N$ weakly interacting electrons (with $N\le 10$) in a two-dimensional parabolic quantum dot with strong Rashba spin-orbit coupling. Using dimensionless parameters for the Coulomb interaction, $\lambda \lesssim 1$, and the Rashba coupling, $\alpha \gg 1$, the low-energy physics is characterized by an almost flat single-particle dispersion. From an analytical approach for $\alpha \to \mathrm{\infty }$ and $N=2$, and from numerical exact diagonalization and Hartree-Fock calculations, we find a transition from a conventional unmagnetized ground state (for $\lambda <{\lambda }_c$) to an orbital ferromagnet (for $\lambda >{\lambda }_c$), with a large magnetization and a circulating charge current. We show that the critical interaction strength, ${\lambda }_c={\lambda }_c(\alpha ,N)$, vanishes in the limit $\alpha \to \mathrm{\infty }$.