Ag 2 S monolayer: an ultrasoft inorganic Lieb lattice.

Lieb lattice, a two-dimensional edge-centered square lattice, has attracted considerable interest due to its exotic electronic and topological properties. Although various optical and photonic Lieb lattices have been experimentally demonstrated, it remains challenging for an electronic Lieb lattice to be realized in real material systems. Here, based on first-principles calculations and tight-binding modeling, a silver sulfide (Ag ₂ S) monolayer is reported as a long-sought-after inorganic electronic Lieb lattice. This Lieb-lattice Ag ₂ S is further found to be ultrasoft, which enables its electronic properties and topological states near the Fermi level to be finely tuned, as evidenced by the strain-induced topologically non-trivial edge states near the valence band edge. These results not only provide an ideal platform to further explore and harvest interesting quantum properties but also pave a way to pursue other inorganic electronic Lieb lattices in a broader material domain.