MATHPH
In the literature: open
Kohn-Luttinger superconductivity from purely repulsive interactions
In plain words
Kohn and Luttinger argued that even purely repelling electrons pair up and superconduct at very low temperature, because the surrounding electrons screen the repulsion unevenly. This has never been proven.
Precise statement
Spin-$1/2$ fermions in $R^{3}$ (or on $Z^{2}$ at generic filling) with weak repulsive short-range v. Prove that the ground state, or the Gibbs state below some $T_c > 0$, has off-diagonal long-range order in the pair density matrix in a channel of nonzero angular momentum. Answer: a proof, with $T_c$ exponentially small in $1/\lambda$.
What would settle it
A proof of pair off-diagonal long-range order for a purely repulsive model.
See also
- Related Superconductivity from repulsion in a single-flavor graphene band
- Related Maximum $T_c$ from purely repulsive electron interactions
- Related Off-diagonal long-range order in a many-body model of attractive fermions
- Related Fermi-liquid behavior of weakly interacting fermions above the pairing scale