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

The exchange and correlation Exc of strongly correlated electrons in two-dimensional (2D) layers of finite width are studied as a function of the density parameter rₛ, 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 thex-y plane. The correlation energy Ec of the quasi-2D system is presented as an interpolation between a one-dimensional (1D) gas of electron-rods (for w∕rₛ>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∕rₛ is small. Results for the Exc(rₛ,ζ,T), the transition to a spin-polarized phase, the effective mass m*, the Land\'e g-factor, etc., are reported here.