EXCHANGE-CORRELATION ENERGY OF A QUASI-2-DIMENSIONAL ELECTRON-GAS - AHARTREE SELF-CONSISTENT APPROACH

We present an approach to the exchange-correlation energy of an electr on gas confined in a finite-width quantum well, which avoids the local -density approximation. We focus on densities large enough to have ele ctrons in more than one subband. This imposes a self-consistent treatm ent of the Hartree interaction (i.e., q = 0 excitation processes) whil e the q not equal 0 interaction can be treated perturbatively. By writ ing the Hamiltonian in terms of appropriate Hartree self-consistent cr eation operators, we can cancel most but not all q = 0 Coulomb contrib utions; a few mixed (q = 0,q not equal 0) terms do remain in the corre lation energy. A numerical calculation of the exchange energy shows th at the effect of the Hartree processes turns out to stay rather small in the whole two-subband filling domain.