Emergence of superconductivity in a doped single-valley quadratic band crossing system of spin-12 fermions

Kelly Ann Pawlak; James M. Murray; Oskar Vafek

doi:10.1103/PhysRevB.91.134509

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Emergence of superconductivity in a doped single-valley quadratic band crossing system of spin-12 fermions

Kelly Ann Pawlak, James M. Murray, Oskar Vafek

DOI 10.1103/PhysRevB.91.134509 · Physical Review B

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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 kagome lattices. In fourfold-symmetric systems, we find that d- and s-wave superconductivity are realized for short-ranged (Hubbard) and longer-ranged (forward scattering) interactions, respectively. In the sixfold-symmetric case, we find either s-wave superconductivity or no superconducting instability.