When Does a Single Repulsive Dirac Cone Superconduct?
Oral-In-person
Abstract
Superconductivity in a single two-dimensional Dirac cone 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.
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.
–
Publication: https://arxiv.org/pdf/2508.13271
Presenters
-
Omid Tavakol
- University of California, Irvine