Exchange-correlation energy functionals for electrons in two dimensions

Two-dimensional (2D) electronic systems have attracted vast interest since the beginning of semiconductor technology. The investigation of electronic properties of these 2D structures form a significant part of condensed matter and materials physics research. Among the available theoretical and computational methods to deal with many-electron systems is the density-functional theory (DFT). The fundamental quantity in DFT is the exchange-correlation (xc) energy functional, which embodies all the effect of the electron-electron interactions. In practice, this functional needs to be approximated. Many approximations have been developed for three-dimensional (3D) systems, where considerable advances beyond the commonly used local spin-density approximation (LSDA) were achieved. Unfortunately, most of the popular 3D approximations are inadequate for 2D systems. Hence, there is a clear need for new approximations specifically developed for 2D systems. Following this important need, efficient and practical expressions for the xc-energy of electrons in 2D are presented. Numerical results for finite systems show that the proposed functionals outperform the standard 2D LSDA.