Pairing around a single Dirac point: A unifying view of Kohn-Luttinger superconductivity in Chern bands, quarter metals, and topological surface states

Abstract

Superconductivity of a single two-dimensional Dirac fermion offers a natural route to topological superconductivity. While usually considered extrinsic—arising from proximity to a conventional superconductor—we investigate when a doped Dirac cone can spontaneously develop superconductivity from a short-range repulsive interaction U via the Kohn–Luttinger mechanism. We show that an ideal, linear Dirac cone is immune to pairing at leading order in U2. Superconductivity instead emerges only through higher-order in k corrections to the dispersion, which are unavoidable in any lattice realization and crucially dictate the pairing symmetry. The form of the pairing thus reflects how the well-known obstruction to realizing a single Dirac cone on a lattice is circumvented. When a Dirac cone arises from broken time-reversal symmetry—for instance, at a transition between Chern insulators or in a valley-polarized phase—we find a topological p−ip state whose chirality is opposite to that of the parent chiral metal above Tc. By contrast, for a surface Dirac cone of a 3D topological insulator, superconductivity is stabilized by anisotropies in the dispersion. For C3v-symmetric warping, as in Bi2Te3, pairing is strongest when the Fermi surface becomes hexagonal, leading to order in the (d±id)×(p+ip) channel with accidental near-nodes. In the highly anisotropic limit vx≫vy, relevant to side surfaces of layered materials, the Fermi surface splits into two branches, and nesting favors a pairing symmetry Δ∼sgn(kx)cos(ky) reminiscent of organic superconductors.

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