Theory of coexisting superconductivity and excitonic pairing in a doped double-layer system under external bias

Abstract

We study a double-layer square-lattice system with intralayer electron–-phonon coupling. Superconducting and excitonic pairings, as well as their coexistence, are examined as functions of key physical parameters, including temperature, intralayer and interlayer Coulomb interactions, electron–phonon coupling strength, doping, and the applied electric field. Superconductivity is shown to emerge from the coupling of intralayer phonons with the total charge density in the layers, resulting in a modification of the total electronic energy of the system. These results provide new insights into the possible mechanism of superconductivity in high-T\(_{C}\) cuprate superconductors.