Electronic Structure and Minimal Models for Flat and Corrugated CuO Monolayers: An Ab Initio Study

[Formula: see text] atomic thin monolayer ([Formula: see text]) was synthesized recently. Interest in the [Formula: see text] is based on its close relation to [Formula: see text] layers in typical high temperature cuprate superconductors. Here, we present the calculation of the band structure, the density of states and the Fermi surface of the flat [Formula: see text] as well as the corrugated [Formula: see text] within the density functional theory (DFT) in the generalized gradient approximation (GGA). In the flat [Formula: see text] , the [Formula: see text]- [Formula: see text] band crosses the Fermi level, while the [Formula: see text]- [Formula: see text] hybridized band is located just below it. The corrugation leads to a significant shift of the [Formula: see text]- [Formula: see text] hybridized band down in energy and a degeneracy lifting for the [Formula: see text]- [Formula: see text] bands. Corrugated [Formula: see text] is more energetically favorable than the flat one. In addition, we compared the electronic structure of the considered [Formula: see text] monolayers with bulk [Formula: see text] systems. We also investigated the influence of a crystal lattice strain (which might occur on some interfaces) on the electronic structure of both [Formula: see text] and determined the critical strains of topological Lifshitz transitions. Finally, we proposed a number of different minimal models for the flat and the corrugated [Formula: see text] using projections onto different Wannier functions basis sets and obtained the corresponding Hamiltonian matrix elements in a real space.