Exploring Monolayer TaF\(_4\) as a 5\(d^1\) Analog to Cuprates with Potential for High-T\(_c\) Superconductivity

The quest for cuprate-like materials has gained momentum from recent research on infinite-layer nickelates. TaF\(_4\), with its structure of tantalum-centered fluorine octahedra, could potentially function as a \(5d^1\) analog to cuprates. According to density functional theory (DFT), monolayer TaF\(_4\) approximates a \(d^{1}\) state, with the \(5d_{xy}\) orbital of Ta almost half-filled. The Fermi level is intersected with a band derived from the \(5d_{xy}\) orbital, resulting in a square-shaped Fermi surface. Energetically, the checkerboard AFM configuration is most favorable, leading to an AFM insulating state upon inclusion of Coulomb interaction. The RPA calculations show that spin susceptibility has notable \((\pi ,\pi )\) peaks, and the \(d_{x^2-y^2}\)-wave pairing exhibits the highest eigenvalue compared to other pairing types. The structural and electronic parallels between TaF\(_4\) and cuprates highlight its potential for high-T\(_c\) superconductivity, although definitive evidence will require further theoretical and experimental validation.