Theory of a Competitive Spin Liquid State for Weak Mott Insulators on the Triangular Lattice

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[Pd(dmit)$_{2}$]$_{2}$. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum $\vec{k}=0$. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.