Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

The exchange and correlation E_xc of strongly correlated electrons in two-dimensional (2D) layers of finite width are studied as a function of the density parameter r_s , spin-polarization ζ and the temperature T . We explicitly treat strong-correlation effects via pair-distribution functions, and introduce an equivalent constant-density approximation (CDA) applicable to all the inhomogeneous densities encountered here. The width w defined via the CDA provides a length scale defining the z -extension of the quasi-2D layer resident in the x-y plane. The correlation energy E_c of the quasi-2D system is presented as an interpolation between a one-dimensional (1D) gas of electron-rods (for w/r_s>1 ) coupled via a log(r) interaction, and a three-dimensional (3D) Coulomb fluid closely approximated from the known three-dimensional correlation energy when w/r_s is small. Results for the E_xc(r_s,ζ,T) , the transition to a spin-polarized phase, the effective mass m^* , the Landé g -factor, etc., are reported here.