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 $\alpha\to \infty$ 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 $\alpha\to \infty$.