First-principles study of two-dimensional electron gas on a layered Gd2C electride surface

Electrides are ionic compounds in which electrons behave as anions in the interior of a positively charged framework. As a layered electride, ${\mathrm{Gd}}_{2}\mathrm{C}$ receives attention because of its ferromagnetism. Although previous research has focused on the bulk properties of ${\mathrm{Gd}}_{2}\mathrm{C}$, few studies have focused on ultrathin layers or surfaces for two-dimensional (2D) characteristics. Here, we report a first-principles study of the electronic properties of few-layer ${\mathrm{Gd}}_{2}\mathrm{C}$ structures. ${\mathrm{Gd}}_{2}\mathrm{C}$ has a work function of 3.35 eV. When a layered electride is exfoliated, the interstitial layer becomes a surface and may be exposed to the outside. Because the interlayer region has changed to the surface, the properties of the electron gases once located in the interlayer in the past will also change. We found that the surface anionic electrons accounted for about 25% of the number of electrons in the interlayer region in the absence of an external electric field. When we applied an external electric field, the number of surface electrons increased, and the increase was proportional to the square of the field intensity. Since the electronic properties of 2D materials can be understood through scanning tunneling spectroscopy (STS), we also performed the STS simulations. At $\ensuremath{-}0.9\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$, the STS image was blurred because of surface anionic electrons. In contrast to the spin-up electron, an interlayer band of the spin-down electron crossed the Fermi level in the ultrathin ${\mathrm{Gd}}_{2}\mathrm{C}$ layers. Our findings open a possibility that the spin-polarized electronic gas in the few-layer electride could be used for spintronics.