Emergence of superconductivity in a doped single-valley quadratic band crossing system of spin-1/2 fermions

Abstract: For two-dimensional single-valley quadratic band crossing systems with weak repulsive electron-electron interactions, we show that upon introducing a chemical potential, particle-hole order is suppressed and superconductivity becomes the leading instability. In contrast to the two-valley case realized in bilayer graphene, the single-valley quadratic band touching is protected by crystal symmetries, and the different symmetries and number of fermion flavors can lead to distinct phase instabilities. Our results are obtained using a weak-coupling Wilsonian renormalization group procedure on a low-energy effective Hamiltonian relevant for describing electrons on checkerboard or kagom\'e lattices. In 4-fold symmetric systems we find that $d$-wave and $s$-wave superconductivity are realized for short-ranged (Hubbard) and longer-ranged (forward scattering), respectively. In the 6-fold symmetric case, we find either $s$-wave superconductivity or no superconducting instability.