Exploring stable Lieb lattices in two-dimensional binary metal-inorganic frameworks: a high-throughput screening approach

The Lieb lattice is fundamental in condensed matter physics for hosting exotic electronic and topological states. Through high-throughput computational screening of 1470 binary metal-inorganic frameworks (MIFs), we identified 24 stable Lieb lattice structures, including 22 new materials. These comprise 15 nonmagnetic, 2 ferromagnetic (FM) half-metals, and 7 antiferromagnetic semiconductors, with critical temperatures reaching 877 K. Key electronic features include flat bands, Dirac cones, and van Hove singularities. HfCl₂ and WO₂ are FM half-metals with large spin gaps (5.37 eV and 3.57 eV), enabling full spin polarization. Be₂C and ReF₂ exhibit nodal loops and quasi-flat bands, respectively, hosting nontrivial topology confirmed by edge-state analysis. Nine MIFs are zero-dimensional electrides with work functions as low as 2.64 eV. Thirteen structures are ground-state phases, ensuring stability. These Lieb lattices offer promising platforms for high-temperature electronic, spintronic, and topological applications.