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Recent quantum gas experiments are ushering in an era of fine-tailoredtwo-body interactions. These include for example atoms with long-rangedipole-dipole interactions and Rydberg-dressed atoms created by opticalcoupling to highly excited electronic states. These systems differ from the``canonical system" of cold atoms with contact interactions characterized by asingle parameter, the scattering length. Inspired by these experiments withcontrollable atomic interactions, here we consider a model many-body system ofspinless Fermi gas in two dimensions, where the bare two-body interaction takesthe form of a soft-core disk potential. We show that the repulsive interactioncan drive the system to a series of nontrivial superfluid states with higherpartial wave paring, for example in the $f$- and $h$-wave channels instead ofthe $p$-wave channel. The zero temperature phase diagram is obtained bynumerical functional renormalization group (FRG), which goes beyond leadingorder perturbation theory and retains the interaction vertices in all channels.We also carry out a perturbative analysis which is justified in the dilutelimit and show that the second order Kohn-Luttinger diagrams provide aqualitative understanding of the onsets of the various superfluid phases. Theperturbative arguments however fail to capture the quantitative phaseboundaries predicted by FRG. Our findings illustrate that the shape of the bareatomic interaction matters in producing the pairing glue in repulsive Fermigases, and tuning the interaction potential offers a promising route to realizeexotic many-body phases in cold atomic gases.

Emergence of pairing glue in repulsive Fermi gases with soft-core interactions