The stability and electronic structure of anti-MXenes

Anti-MXenes is a new class of 2D materials with the formula MₙXₙ₊₁, and has recently been attracting attention. The successful synthesis of Mo₅N₆ and the identification of its atomic arrangements (labeled as α and γ), along with the resolved structure of TiC₂, raise an important question: What are the possible atomic structures of MₙXₙ₊₁ layers across different transition metals M and values of n? In this work, we identify a new structural prototype, denoted as β, through a combination of density functional theory (DFT) calculations and evolutionary optimization. By systematically exploring the stable polymorphs of 32 anti-MXenes structures with the formula MₙXₙ₊₁ (M = Ti, V, Cr, Mn, Nb, Mo, Ta, and W, $n = 2, 3, 4, 5$), we find that the β structure is more favorable in thinner compositions ($n = 2$) and tends to appear at outermost layers of thicker structures ($n = 5$), leading to hybrid structures that are mixtures of α/γ and β configuration. We identify a range of non-trivial electronic states in these materials: semimetals, flat bands, a semiconductor and materials with high electronc density at the Fermi level. Further analysis of M₂X₃ β structures using supercell models reveals that Mo₂X₃ relaxes into a different lower energy configuration. Our findings unveil the rich and complex structural and electronic landscape of anti-MXenes, which warrant further exploration of this class of materials.