We calculate the $r_s$ expansion of the ground-state energy per particle of a two-dimensional electron gas with spin-orbit interaction induced by the Rashba coupling. At high areal electron density, we obtain the energy for noninteracting electrons, their exchange energy, and the lowest-order approximation for the correlation energy. A closed-form expression is obtained for the energy of noninteracting electrons. However, we must calculate the exchange and correlation energy numerically. As the density is increased and $r_s$ decreases, the ground-state energy changes rapidly at some value $r_s=r_s^{*}$ and the Fermi energy $E_F$ changes from negative to positive. When $E_F<0$, only the lower spin subband is occupied. An interesting effect occurs in the presence of electron-electron interaction as $E_F$ increases through $E=0$ and the upper spin subband suddenly gets a finite population rather than increasing gradually.

• Received 17 October 2005

DOI:https://doi.org/10.1103/PhysRevB.73.165315