Cooper Pair with Nonzero Momentum in System with Spin Dependent Mass of Quasiparticles

We consider a single Cooper pair with the spin dependent quasiparticle masses, with and without applied magnetic field. Such situation takes place for the strongly correlated electron systems, where a relatively strong Hubbard interaction differentiates the quasiparticle states in the majority- and the minority-spin subbands. In that situation, the two spin subbands in an applied magnetic field are not only shifted one with respect to the other, but also distorted differently, which results from the electronic correlations. Under these circumstances, the fermionic particles composing the Cooper pair, are quantum mechanically distinguishable. In result, the Cooper pair has a nonzero momentum (i.e. produces a stationary current in a similar manner as electron in the Bloch state), and there exists a critical value of the attractive interaction, below which the bound Cooper-pair state is not formed. The presence of the applied field (included via the Zeeman term) does not alter the picture qualitatively. Importance of these results for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov phase in strongly correlated systems is mentioned.