Semimetallic bands derived from interlayer electrons in the quasi-two-dimensional electride ${\mathrm{Y}}_2\mathrm{C}$

Two-dimensional (2D) electrides are a new concept material in which anionic electrons are confined in the interlayer space between positively charged layers. We have carried out angle-resolved photoemission spectroscopy measurements on ${\mathrm{Y}}_2\mathrm{C}$, which is a possible 2D electride, in order to verify the formation of 2D electride states in ${\mathrm{Y}}_2\mathrm{C}$. We clearly observe the existence of semimetallic “electride bands” near the Fermi level, as predicted by ab initio calculations, which conclusively demonstrates that ${\mathrm{Y}}_2\mathrm{C}$ is a quasi-2D electride with electride bands derived from interlayer anionic electrons.

Figure 1

(a) Crystal structure of ${\mathrm{Y}}_2\mathrm{C}$ together with the schematic of the anionic electron layer. Solid thick lines represent the conventional hexagonal unit cell of rhombohedral ${\mathrm{Y}}_2\mathrm{C}$. Ab initio calculations predict that anionic electrons $2{\mathrm{e}}^{-}$ are confined in the interlayer space between the ${\left[{\mathrm{Y}}_2\mathrm{C}\right]}^{2+}$ sheets. (b) Band structure of ${\mathrm{Y}}_2$ calculated by the PAW method. The interlayer probability, i.e., the probability of the electron being found in the interlayer space, is represented by the size of the filled circles. Semimetallic “electride bands” are formed near $E_F$. The inset shows the BZ for the rhombohedral lattice of ${\mathrm{Y}}_2\mathrm{C}$ together with the symmetry points.

Figure 2

(a) LEED pattern for a cleaved surface of ${\mathrm{Y}}_2\mathrm{C}$ single crystal acquired at an electron energy of 124 eV. Dotted lines represent the hexagonal surface BZ. (b) Out-of-plane FS map in the $\mathrm{\Gamma }ZFL$ plane obtained by varying the excitation photon energy from 380 to 500 eV. The FS map was obtained by plotting the ARPES intensity within the energy window of $\pm 100$ meV from $E_F$. The dotted lines indicate the BZ boundaries, while red solid lines indicate the electron FS obtained by FLAPW calculations. The orange lines represent the $\mathit{k}$ path passing through the $L$ point (at a photon energy of 400 eV) and the $F$ point (at a photon energy of 440 eV). (c), (d) In-plane FS maps acquired at constant photon energies of 400 eV (c) and 440 eV (d) by changing emission angles. Calculated FSs in plane $(k_x\text{−}{k}_y$ plane) crossing the $L$ point $(k_z=29.5$ $[2\pi /c])$ and the $F$ point $(k_z=31.0$ $[2\pi /c])$ are superimposed on (c) and (d), respectively. Red and blue lines show electron and hole pockets, respectively.

Figure 3

(a) Measured $\mathit{k}$ path passing through the $F$ point in the rhombohedral BZ for which ARPES measurements were carried out at $h\nu =440$ eV, which corresponds to the orange line in Fig. 2. (b) Experimental band structure obtained by plotting the second derivative of the ARPES spectra acquired along the $\mathit{k}$ path in (a). The energy bands along the $Z\text{−}F\text{−}Z$ direction calculated by the FLAPW method are superimposed by solid lines. Filled triangles indicate the Fermi momentum $\left(k_F\right)$ determined by ARPES spectra [28]. (c) ARPES spectra near $E_F$ and around the $F$ point. Thick red lines indicate the ARPES spectra at $k_F$.

Figure 4

(a) Measured $\mathit{k}$ path passing through the $B$ point of the rhombohedral BZ for which ARPES measurements were carried out at $h\nu =456$ eV. (b) Experimental band structures obtained by plotting the second derivative of ARPES spectra. Solid lines indicate the energy bands calculated by the FLAPW method along the $B\text{−}Z\text{−}B$ direction. Filled triangles indicate the $k_F$ points determined by ARPES spectra [28]. (c) ARPES spectra near $E_F$ and around the $B$ point. The thick red line indicates the ARPES spectrum at $k_F$.