Screening phonon-mediated superconductors from static orbital Hamiltonians

The first-principles search for superconductors is severely limited by the high cost of electron-phonon coupling (EPC) calculations. Here we develop a low-cost, physically transparent framework that identifies strong-EPC materials directly from static orbital-based Hamiltonians without explicit phonon perturbation calculations. Verification using density functional perturbation theory (DFPT) for representative superconductors shows that the framework captures semi-quantitatively the EPC scale at substantially lower computational cost. Applied to more than 36,000 compounds in the MattKeyBond database, it identifies 34 dynamically stable superconducting candidates with calculated $T_c > 10$ K after DFPT verification. These candidates reveal two distinct routes to relatively high-$T_c$ superconductivity: a metallized covalent $\sigma$-bond route that is more favorable for achieving high-$T_c$ superconductors, and a Fermi-level density-of-states accumulation route that can enhance $T_c$ but usually to a more limited extent.