Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice

The particles in the honeycomb lattice with on-site s-wave pairing exhibit many interesting behaviors, which can be described in the framework of the Hubbard model. Among others, at the half-filling, some critical value |U-c| of pairing interaction U < 0 exists that, for U < U-c, the superconducting phase becomes unstable. Introduction of the nonzero hopping t ' between next-nearest-neighbor sites strongly modifies the physical properties of the system. Here, we discuss the behavior of the system for t ' not equal 0 (at the ground state), where the hopping between next-nearest neighbors leads to change of the order of phase transition between superconducting and normal phases from discontinuous to continuous one in the external magnetic field h. We show that this behavior is strongly dependent on t ' and associated with the Dirac cones in the non-interacting band structure of the system. For non-zero magnetic field and for some range of t ', a spin-polarized superconducting phase occurs in the ground state phase diagram (only at the half-filling and for h not equal 0).