\eta-superconductivity in the Hubbard chain with pair hopping
  The ground state phase diagram of the 1D Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper pair center-of-mass momentum Q=0 (BCS-\eta_0 phase) and Q=\pi (\eta_\pi-phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator as well as an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting BCS-\eta_0 and \eta_\pi phases and the metallic Luttinger-liquid phase. The BCS-\eta_0 phase exhibits smooth crossover from a weak-coupling BCS type to a strong coupling local-pair regime. The \eta_\pi phase shows properties of the doublon (zero size Cooper pair) superconductor with Cooper pair center-of-mass momentum Q=\pi. The transition into the \eta_\pi- paired state corresponds to an abrupt change in the groundstate structure. After the transition the conduction band is completely destroyed and a new \eta_\pi-pair band corresponding to the strongly correlated doublon motion is created. 
G.I. Japaridze, A.P. Kampf, M. Sekania, P. Kakashvili, and Ph. Brune