Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to $kappa-(BEDT-TTF)_2 Cu_2 (CN)_3$

Recent experiments on the organic compound $kappa-(BEDT-TTF)_2 Cu_2 (CN)_3$ raise the possibility that the system may be described as a quantum spin liquid. Here we propose a pairing state caused by the `Amperean attractive interaction between spinons on a Fermi surface mediated by the U(1) gauge field. We show that this state can explain many of the observed low temperature phenomena and discuss testable consequences.