Cross Dimensionality and Emergent Nodal Superconductivity with p-orbital Atomic Fermions

I study cross dimensionality of $p$-orbital atomic fermions loaded in an optical square lattice with repulsive interactions. The cross-dimensionality emerges when the transverse tunneling of $p$-orbital fermions is negligible. With renormalization group analysis, the system is found to support two dimensional charge, orbital, and spin density wave states with incommensurate wavevectors. The transition temperatures of these states are controlled by perturbations near a one dimensional Luttinger liquid fixed point. Considering transverse tunneling, the cross-dimensionality breaks down and the density wave (DW) orders become unstable, and I find an unconventional superconducting state mediated by fluctuation effects. The superconducting gap has an emergent nodal structure determined by the Fermi momentum, which is tunable by controlling atomic density. Taking an effective description of the superconducting state, it is shown that the nodal structure of Cooper pairing can be extracted from momentum-space radio-frequency spectroscopy in atomic experiments. These results imply that $p$-orbital fermions could enrich the possibilities of studying correlated physics in optical lattice quantum emulators beyond the single-band Fermi Hubbard model.