Tunable Superconductivity Mediated by Heavy-Electron Plasmons: Band-Structure and Quantum-Geometric Engineering

Abstract

Conventional superconductivity derives its pairing glue from lattice vibrations, tying its characteristic scales to chemistry and atomic masses. Plasmons$-$the collective oscillations of electrons$-$can instead be reshaped through electronic structure engineering, but the principles governing optimal plasmon-mediated pairing remain unclear. Here, we establish such principles for two-carrier systems in which heavy-electron plasmons mediate the pairing of light electrons. Within the random-phase approximation and Eliashberg theory, we calculate the optimal $T_c$ of minimal metallic models and show that it is controlled by a competition between the plasmon energy scale and retardation-driven suppression of the repulsion, yielding optimal carrier densities and band masses. While the plasmon channel alone reaches only $T_c\sim$ 0.1 K, a moderate phonon attraction cooperates with it, boosting $T_c$ by two orders of magnitude to above 20 K. However, the band flattening needed for slow metallic plasmons also favors the development of competing orders. We therefore consider an insulating system in which coherent interband transitions between flat bands generate gapped interband plasmons without free carriers. The heavy-band quantum metric governs the dispersion and electron-plasmon pairing strength of the interband plasmon, while the quantum geometry of the light band suppresses static screening and enhances the net attraction. Because layer separation rapidly weakens pairing, we propose systems with coexisting light and heavy electrons living in different mirror-symmetry sectors of the same layer as promising platforms. Our results establish a new role for flat-band systems in superconductivity: rather than hosting the paired electrons themselves, they can serve as a tunable pairing mediator whose collective charge excitations set the superconducting energy scale beyond their narrow bandwidth.