η-pairing on square and triangular lattices

The $\ensuremath{\eta}$-pairing is a type of Cooper pairing state in which the phase of the superconducting order parameter is aligned in a staggered manner, in contrast to the usual BCS superconductors with a spatially uniform phase. In this study, we search for a characteristic $\ensuremath{\eta}$-pairing state in a triangular lattice where a simple staggered alignment of the phase is not possible. As an example, we consider the attractive Hubbard model on both the square and triangular lattices under a strong external Zeeman field. Using the mean-field approximation, we have identified several $\ensuremath{\eta}$-pairing states. Additionally, we have examined the electromagnetic stability of the pairing state by calculating the Meissner kernel. Odd-frequency pairing plays a crucial role in achieving a diamagnetic response if the electrons experience a staggered superconducting phase during the propagation of current.