Spin-charge separation and unconventional superconductivity in the t − J model on the honeycomb lattice

The physical nature of doped Mott insulators has been the subject of intensive study for decades. The single-band Hubbard model and the $t\text{\ensuremath{-}}J$ model on a bipartite lattice are widely recognized as the simplest models to describe these materials. However, the key mechanism of superconductivity in these toy models remains unclear. Here we propose a novel mechanism for the ($d+id$)-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t\text{\ensuremath{-}}J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. In the presence of anti-ferromagnetic order near half-filling, we develop a continuum effective field theory for holons, which reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. When $t/J$ is large, the repulsive interaction dominates, leading to a non-Fermi liquid behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Potential theoretical and experimental methods to validate the mechanism are discussed.