Extended Data Fig. 1: Crystal structure of the 2D [Gd₂C]²⁺·2e⁻ electride.

a, Schematic illustration of the 2D quantum electron liquid on the surface of [Gd₂C]²⁺·2e⁻ electride. It has anti-CdCl₂-type layered structure with a space group of R\(\bar 3\)m. The cationic slab [Gd₂C]²⁺ is composed of an edge-sharing octahedra structure and is separated by the interlayer space. IAEs (brown arrow) are confined between the positively charged [Gd₂C]²⁺ layers. The 2D electrons distinct from IAEs are floated on the topmost [Gd₂C]²⁺ layer. The purple lines indicate the unit cell. b,c, Photographs of single crystal [Gd₂C]²⁺·2e⁻ rod with 50 mm length grown by floating zone melting method (b) and as-cleaved crystal by 3 M Scotch tape (c). d, Lattice parameters obtained by the XRD measurements¹⁹ and the DFT calculations.