When Flat Bands Meet Soft Phonons: A Synergistic Mechanism for Enhanced Superconductivity in Boron–Carbon Clathrates

Abstract Boron–carbon clathrates, represented by SrB3C3, are emerging as a promising family of phonon-mediated conventional superconductors with high critical temperatures (Tc) under ambient pressure. Substituting Sr with other metals has been extensively explored to enhance superconductivity; however, the underlying mechanism of the Tc variation remains elusive. We demonstrate a strong non-monotonic increase in Tc upon hole doping due to synergy between flat bands and soft phonons in these systems. Employing ab initio calculations, we uncover a host–guest interaction between the clathrate framework and the metal atoms through charge transfer. The metal atoms affect the clathrate properties by varying the occupancy of the B–C bonding states, tuning the Fermi level and regulating the phonon frequencies. On the one hand, B–C clathrates form two flat bands due to the lattice symmetry, enhancing the electron-phonon coupling (EPC) when the Fermi level crosses the bands. On the other hand, the EPC strength is anti-correlated with the characteristic vibrational frequency via a phonon-softening mechanism. These two factors jointly result in a non-monotonic dependence of Tc on the Fermi level, and hole doping increases Tc significantly because of the synergy between flat bands and soft phonons. This work establishes a unified picture of the superconductivity in B–C clathrates and guides the rational design of novel superconducting materials.