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$η$-pairing superfluid in periodically-driven fermionic Hubbard model with strong attraction

We propose a novel possibility of dynamically changing the pairing of superconductors from $s$ wave to $η$ pairing (where the pairs condense at the Brillouin-zone corner momenta) by driving the system with ac fields. We consider a periodically-driven attractive Hubbard model in the strong-coupling regime, and show that the pair-hopping and pair-repulsion terms in the effective Hamiltonian in the Floquet formalism are drastically renormalized in different manners between the two terms, which can change the ground states from an $s$-wave superconductivity to an $η$-pairing superconductivity or a charge-ordered phase. While in isolated systems such as cold atoms a simple quench scheme would not realize the dynamical phase transition into $η$ pairing, we show that there are pathways that realize the dynamical transition, where the field amplitude is varied via a charge-ordered phase as an intermediate state.