Real-space orbital tiling approach for the classification and design of superconductors

Despite substantial advances in condensed matter physics, we still lack a predictive framework capable of guiding the discovery of new families of superconductors. While momentum-space approaches have advanced the microscopic understanding of superconductivity, they offer limited guidance for materials design. Here, we propose a real-space framework which conceptualizes Cooper pairs as confined standing waves along coherent tilings of atomic orbitals. We call this model the real-space orbital superconducting pathway (ROSP). Using a tight-binding toy model, we show that the energetics of electron pairing depend on the configuration and overlap of real-space orbitals, which motivates<i>a priori</i>design of superconducting families from orbital tiling. We then extend Roald Hoffmann's isolobal analogy to the ROSP framework. In this formulation, molecular fragments within extended solids are treated as isolobal when they share analogous frontier orbital character, and superconducting pathways are treated as isolobal when their real-space orbital tiling and connectivity are analogous. Under this scheme, superconducting families are grouped by shared orbital pathway architecture rather than by crystallographic similarity or nominal electron count, as in conventional isostructural or isoelectronic approaches. As an example of the utility of this approach, we propose that the ROSP in the candidate superconductor material Sr2CoO2(CN)2would be isolobal to that in Sr2CuO2(Cl)2. We also introduce a notation for classifying ROSPs and identify several new ROSP families on square net and kagomé lattices. This framework offers a new route to predicting and designing high-<i>T</i>_<i>c</i>superconductor families, based solely on real-space orbital architecture, even in the absence of microscopic knowledge of the pairing interaction.