Emergent interlayer nodal superfluidity of a dipolar fermi gas in bilayer optical lattices

Understanding the interplay between magnetism and superconductivity is one of the central issues in condensed matter physics. Such interplay induced nodal structure of superconducting gap is widely believed to be a signature of exotic pairing mechanism (not phonon mediated) to achieve unconventional superconductivity, such as in heavy fermion, high $T_c$, and organic superconductors. Here we report a new mechanism to drive the interplay between magnetism and superfluidity via the spatially anisotropic interaction. This scheme frees up the usual requirement of suppressing long-range magnetic order to access unconventional superconductivity like through doping or adding pressure in solids. Surprisingly, even for the half-filling case, such scheme can lead the coexistence of superfluidity and antiferromagnetism and interestingly an unexpected interlayer nodal superfluid emerges, which will be demonstrated through a cold atom system composed of a pseudospin-$1/2$ dipolar fermi gas in bilayer optical lattices. Our mechanism should pave an alternative way to unveil exotic pairing scheme resulting from the interplay between magnetism and superconductivity or superfluidity.