Exchange-correlation energy of a multicomponent two-dimensional electron gas

We discuss the exchange-correlation energy of a multicomponent (multi-valley) two-dimensional electron gas and show that an extension of the recent parametrisation of the exchange-correlation energy by Attacalite et al (Phys. Rev. Lett. 88, 256601 (2002)) describes well also the multicomponent system. We suggest a simple mass dependence of the correlation energy and apply it to study the phase diagram of the multicomponent 2D electron (or hole) gas. The results show that even a small mass difference of the components (e.g. heavy and light holes) decreases the concentration of the lighter components already at relatively high densities.