Interaction-driven Weyl superfluids from topologically trivial bands in an optical Raman lattice

Abstract

We propose a scheme to realize Weyl superfluidity from topologically trivial bands in the strongly correlated regime of a three-dimensional optical Raman lattice. The scheme builds on a pairing mechanism arising from the interplay between a large Zeeman splitting and strong Hubbard interaction. Spin-flip hopping suppressed by the large Zeeman detuning is resonantly restored when the attractive Hubbard interaction compensates the energy mismatch, yielding a correlated spin-orbit coupling that depends on the local particle configuration. Combining this density-dependent in-plane spin-orbit coupling with density-dependent spin-conserving interlayer tunneling extends the pairing mechanism to three dimensions. A self-consistent mean-field treatment of the microscopic model yields Weyl superfluids with two, four, or eight nodes, together with fully gapped weak topological superfluids. Tuning the interaction strength and particle filling drives transitions between these phases and controls the number of Weyl nodes. We further propose an experimental implementation with ultracold $^{40}\mathrm{K}$ atoms. Our results highlight density-assisted spin-orbit coupling as a mechanism for realizing Weyl superfluidity in strongly correlated systems.