We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the η phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows to determine optimal regimes for the FFLO phase as well as η-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T = 0. Finally, the obtained results show that despite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.

In this paper we address Lifshitz transition induced by applied external magnetic field in a case of iron-based superconductors, in which a difference between the Fermi level and the edges of the bands is relatively small. We introduce and investigate a two-band model with intra-band pairing in the relevant parameters regime to address a generic behaviour of a system with hole-like and electron-like bands in external magnetic field. Our results show that two Lifshitz transitions can develop in analysed systems and the first one occurs in the superconducting phase and takes place at approximately constant magnetic field. The chosen sets of the model parameters can describe characteristic band structure of iron-based superconductors and thus the obtained results can explain the experimental observations in FeSe and Co-doped BaFe2As2 compounds.

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The paper is devoted to a study of superconducting properties of population-imbalanced fermionic mixtures in quasi-one-dimensional optical lattices. The system can be effectively described by the attractive Hubbard model with the Zeeman magnetic field term.