Kohn-Luttinger superconductivity at low density: On the importance of interband polarization

We investigate superconductivity in two-dimensional topological states at low density through the Kohn-Luttinger (KL) mechanism, employing both analytical and numerical methods to assess superconducting instabilities. Our study examines both interband and intraband scattering processes by modeling graphene as a four-band system and the surface of a topological insulator as a two-band system using a single Dirac Hamiltonian. Our analysis reveals that the primary contribution to superconductivity originates from electron polarization deep within the Fermi sea, rather than from polarization near the Fermi surface. Additionally, we find that in graphene, valley scattering enhances superconducting tendencies, a phenomenon not observed in the single Dirac Hamiltonian case. These insights highlight the significant role of interband scattering and the impact of valley effects on superconductivity in these systems.