Revision 1

Accepted · first revision · record

Title: Kohn-Luttinger superconductivity from purely repulsive interactions
Plain: 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: 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 $1/\lambda$.
Settled by: A proof of pair off-diagonal long-range order for a purely repulsive model.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 1965