First-principles study of two-dimensional electron gas on a layered ${\mathrm{Gd}}_2\mathrm{C}$ 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 $-0.9\mathrm{eV}$, 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.

Figure 1

Optimized structure of few-layered ${\mathrm{Gd}}_2\mathrm{C}$. In this figure, gray color indicates the Gd atom, and black is the carbon atom. (a) ABC-stacked bulk, (b) monolayer ($N=1$), (c) bilayer ($N=2$), (d) trilayer ($N=3$), (e) tetralayer ($N=4$), and (f) pentalayer ($N=5$) of ${\mathrm{Gd}}_2\mathrm{C}$. (g) Top view of the ${\mathrm{Gd}}_2\mathrm{C}$ bilayer ($2\times 2$ supercell). $N$ represents the number of layers. The numbers denote the distances ($\mathrm{\Delta }z$) in the $z$ direction in the unit of Å. In (g), the numbers represent the distance in the lateral direction ($\mathit{xy}$ directions) in the unit of Å.

Figure 2

(a) DOS plots and (b) electronic band structures of few-layer ${\mathrm{Gd}}_2\mathrm{C}$ systems. Solid (dotted) lines indicate the electronic bands of the spin-up (spin-down) electrons. The blue and green lines denote the bands of IAE states. For comparison, the DOS was divided by $N$, i.e., the number of layers.

Figure 3

(a) Total charge density difference plots of few-layered ${\mathrm{Gd}}_2\mathrm{C}$. (b) Ball-and-stick models show the X and ${\mathrm{X}}^{\prime }$ sites in the bulk. (c) DOS plots of X and ${\mathrm{X}}^{\prime }$ sites. In the DOS plots, the X and ${\mathrm{X}}^{\prime }$ sites are denoted by solid and dotted lines, respectively.

Figure 4

Resurgence of the anionic electrons at the surface by the electric field effect. (a) Spatial positions of the Y, ${\mathrm{Y}}^{\prime }, {\mathrm{Y}}^{\prime \prime }$, X, and ${\mathrm{X}}^{\prime }$ sites. (b) Electronic density difference plot for the mono-, bi-, and trilayer structures under the electric field of 0.1 V/Å. (c) The calculated number ($\mathrm{\Delta }{Q}_{\mathcal{E}}$) of electrons pulled out by the electric field $\mathcal{E}$ in the bilayer. The fitted lines show the quadratic behavior.

Figure 5

The atomic DOS and STS simulation results on the surface of ${\mathrm{Gd}}_2\mathrm{C}$. (a) The atomic DOS of the Y, ${\mathrm{Y}}^{\prime }$, and ${\mathrm{Y}}^{\prime \prime }$ sites for the mono-, bi-, and trilayer systems and (b) the orbital decomposed DOS of the Gd atom at the bilayer surface. In (a), the blue (black, red) line indicates the Y (${\mathrm{Y}}^{\prime }, {\mathrm{Y}}^{\prime \prime }$) site. In (b), the black (red, blue) line indicates the $d_{xy}$ and $d_{x^2-y^2}$ ($d_{xz}$ and $d_{yz}, d_{z^2}$) orbitals of the Gd atom. (c) Simulated STS images of the bilayer ${\mathrm{Gd}}_2\mathrm{C}$ surface. The images were obtained under the constant-height (2 Å) mode from the computational simulations. The rhombus shape in red color represents the unit cell of ${\mathrm{Gd}}_2\mathrm{C}$.

Figure 6

Band structures of few-layer ${\mathrm{Gd}}_2\mathrm{C}$. Solid lines indicate spin-up states in the upper panel, and dashed lines indicate spin-down states in the lower panel. The bands marked with blue and green lines for spin-up and spin-down electrons represent IAE states, respectively.

Figure 7

DOS plot of the difference between the presence and absence of an electric field in the bilayer region. The solid black line represents the DOS for the absence of an electric field, and the dashed lines (red and blue) correspond to the presence of an electric field (0.1 V/Å and 0.4 V/Å). The DOS plot inside the black rectangle in the upper panel is enlarged and shown in the lower panel. The magnified DOS clearly shows the differences in the sites on the surface (Y, ${\mathrm{Y}}^{\prime }$, and ${\mathrm{Y}}^{\prime \prime }$), whereas the differences are not revealed at the sites in the interlayer regions (X and ${\mathrm{X}}^{\prime }$).

Figure 8

STM images of the bilayer in the constant-height (2 Å) mode for each energy range. The red rhombus represents the unit cell of ${\mathrm{Gd}}_2\mathrm{C}$. Triangular patterns appear in the STM images at some energies, and honeycomb patterns appear at other energies.

Figure 9

The spin density plots of the ${\mathrm{Gd}}_2\mathrm{C}$ ultrathin structures (from the monolayer to the pentalayer).