Fluctuation exchange study on the electron-hole asymmetry of the superconductivity across 1/3 filling in the trilayer Hubbard model

Abstract: We study within the fluctuation exchange approximation the trilayer Hubbard model where three layers of the Hubbard model are coupled by large interlayer hoppings so that the overlap of the bonding, nonbonding, and antibonding bands is relatively small. We pay special attention to the band fillings close to 1/3, for which the bonding and nonbonding bands as a whole are close to half filling. For relatively small values of the onsite $U$, superconductivity roughly exhibits electron-hole symmetric behavior, as expected for a nearly half-filled two-band system. By contrast, an asymmetry appears when $U$ becomes large, where superconductivity is more favored in the hole-doped regime, i.e., in the regime where electrons are removed from 1/3 filling. We attribute this asymmetry to the asymmetric renormalization of the bonding, nonbonding, and antibonding bands when $U$ is large.