Novel properties of the Kohn-Sham exchange potential for open systems: Application to the two-dimensional electron gas

The properties of the Kohn-Sham (KS) exchange potential for open systems in thermodynamical equilibrium, where the number of particles is non-conserved, are analyzed with the Optimized Effective Potential (OEP) method of Density Functional Theory (DFT) at zero temperature. The quasi–two-dimensional electron gas (2DEG) is used as an illustrative example. The main findings are that the KS exchange potential builds a significant barrier-like structure under slight population of the second subband, and that both the asymptotic value of the KS exchange potential and the inter-subband energy jump discontinuously at the one-subband (1S) → two-subband (2S) transition. The results obtained in this system offer new insights into open problems of semiconductors, such as the band-gap underestimation and the band-gap renormalization by photo-excited carriers.