Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit

Abstract

The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we determine the potential near the two- and one-dimensional electron gases (EG), doing this analytically at the level of the exact exchange of the density-functional theory (DFT). We find that, at $r_{\perp }\gg k_F^{-1}$, where $r_{\perp }$ is the distance from the EG and $k_F$ is the Fermi radius, the potential obeys the already known asymptotic $-e^2/r_{\perp }$, while at $r_{\perp }\lesssim k_F^{-1}$, but {\em still in vacuum}, qualitative and quantitative deviations of the exchange potential from the asymptotic law occur. The playground of the excitations to the low-lying image states falls into the latter regime, causing significant departure from the Rydberg series. In general, our analytical exchange potentials establish benchmarks for numerical approaches in the low-dimensional science, where DFT is by far the most common tool.

11 pages, 9 figures

References in corpus (5)

• Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential
• Kohn-Sham Exchange Potential for a Metallic Surface
• Asymptotic behavior of the Kohn-Sham exchange potential at a metal surface
• Time-dependent localized Hartree-Fock potential
• On Augmented Kohn-Sham Potential for Energy as a Simple Sum of Orbital Energies

Cited by in corpus (5)

• Quasi-low-dimensional electron gas with one populated band as a testing ground for time-dependent density-functional theory
• Semilocal approximations to the Kohn-Sham exchange potential as applied to a metal surface
• Exact Exchange: a pathway for a Density Functional Theory of the Integer Quantum Hall Effect
• Cross-over between collective and independent-particle excitations in quasi-2D electron gas with one filled miniband
• Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems