New mechanism for unconventional superconductivity from repulsive interaction*

Within five years, the record of the most dilute superconductor has been broken several times, and an increasing number of materials, such as WTe₂, SrTiO₃, or graphitic heterostructures, host superconductivity at extremely low carrier densities. In this regime, however, the standard phonon-mechanism for superconductivity fails as the Fermi energy can be comparable to, or even smaller than, the Debye energy. To theoretically understand the above materials, we need new routes toward superconductivity, which stem from the repulsive Coulomb interaction itself and do not rely on Fermi surface renormalizations.

In this work, we have discovered one such mechanism in a two-dimensional lattice model, whose structure allows for an exact solution. This solution unveils inter-valley pairing upon infinitesimal doping of the conduction band, driving a BCS-BEC crossover as a function of carrier density. The predictions of our model not agree with recent measurements on ZrNCl, such as the presence of pairing for densities as low as 0.2%, the emergence of a BCS-BEC crossover, or the relatively large critical temperature. Our work demonstrates a reliable and robust mechanism for unconventional superconductivity from repulsion in narrow band systems. It also offers a realistic route towards the realization of finite angular momentum superfluidity for spin-polarized fermions.