Hartree-Fock ground state of the two-dimensional electron gas with Rashba spin-orbit interaction

We search for the uniform Hartree-Fock ground state of the two-dimensional electron gas formed in semiconductor heterostructures including the Rashba spin-orbit interaction. We identify two competing quantum phases: a ferromagnetic one with partial spin polarization in the perpendicular direction and a paramagnetic one with in-plane spin. We present a phase diagram in terms of the relative strengths of the Rashba to the Coulomb interaction and the electron density. We compare our theoretical description with existing experimental results obtained in GaAs-AlGaAs heterostructures.

Figure 1

Ground-state phase diagram in the Hartree-Fock approximation in terms of the density parameter $r_s$ and the Rashba to Coulomb energy ratio $p$.

Figure 2

Mean value of the perpendicular spin projection per particle $\left(\hslash =1\right)$ as a function of the Rashba to Coulomb energy ratio in the OP phase.