Superconductivity from orbital-selective electron-phonon coupling in A V3Sb5

Recent experiments have shown that the phase diagrams of the kagome superconductors AV3Sb5 are strongly impacted by changes in the c-axis lattice parameter. Here, we show that c-axis deformations impact primarily the Sb apical bonds and thus the overlap between their pz orbitals. Changes in the latter, in turn, substantially affect low-energy electronic states with significant Sb character, most notably the central electron pocket and the van Hove singularities located above the Fermi level. Based on the orbital-selective character of c-axis strain, we argue that these electronic states experience a non-negligible attractive electron-phonon pairing interaction mediated by fluctuations in the apical Sb bonds. We thus propose a multiband model for superconductivity in AV3Sb5 that includes both the Sb pocket and the V-derived van Hove singularities. Upon comparing the theoretical phase diagram with the experimentally observed vanishing of the Tc dome across a Lifshitz transition of the Sb pocket, we propose that either an s+- or an s++ state is realized in AV3Sb5.