Fermion quartets in a two-band model of superconductivity

• The investigation of a two-band model of superconductivity with fermion pairs and quartets.
• Ground state properties are examined.
• Two gap parameters turn out to be interdependent.
• Pairs and quartets contribute to the induced electric current.
• Quartets can totally suppress pairs.

A two-band superconducting fermion system is investigated. Apart from an on-site two-fermion attraction acting in the wider band an on-site four-fermion attraction is introduced. The four-fermion potential binds four electrons from both of the bands residing on a lattice site into a fermion quartet. Additionally, the local Coulomb repulsion is involved in the narrower band. There exist two order parameters in the system: a conventional BCS-type gap and a quartet one. The ground state properties such as the dependence of these order parameters on the Coulomb repulsion and the four-fermion attraction are examined. Furthermore, the average numbers of electrons constituting the system as functions of the interactions are displayed as well. It is shown that quartet superconductivity is very sensitive to the Coulomb repulsion and when subject to this interaction quartets disappear for quite small values of that. Finally, the response to an external magnetic field is studied. This reveals a quite complicated behavior of the system because in general two electric currents can flow through a specimen but there exist conditions under which one of them disappears. Such a behavior is determined by the dependence of both currents on the strength of the Coulomb repulsion and the four-fermion attraction. Two scenarios with dx2-y2dx2-y2-wave pairing are investigated on an initial stage as well.