FFLO state and anomalous flux quantization in the one-dimensional attractive Hubbard models with imbalanced spin populations

We examine anomalous flux quantization of the one-dimensional attractive Hubbard models with imbalanced spin populations by using the exact diagonalization method. In the single chain Hubbard model with sufficiently large attractive interaction and imbalanced spin populations, the period of the flux quanta is determined by the difference between the system size N_L and electron number N_e as h/(N_L − N_e)e, in contrast to the superconducting flux quanta of h/2e based on usual Cooper pairs and/or the period h/4e derived by the mean-field theory. We find that similar anomalous flux quantization appears in the zigzag and ladder Hubbard models with imbalanced spin populations, when the band structure near the Fermi levels is regarded to be almost equivalent to that of the single chain Hubbard model