Spin-charge separation and unconventional superconductivity in \textit{t}-\textit{J} model on honeycomb lattice

TL;DR

This paper investigates a new mechanism for $d+id$-wave superconductivity in the doped honeycomb lattice $t$-$J$ model, revealing the role of spin-charge separation and holon interactions through numerical and theoretical analysis.

Contribution

It introduces a novel $d+id$-wave superconductivity mechanism in the honeycomb $t$-$J$ model based on Grassmann tensor states and spin-charge separation, with a developed effective field theory.

Findings

Holon interactions are influenced by spinon and gauge fluctuations.

Large $t/J$ leads to non-Fermi liquid behavior due to repulsive holon interactions.

Moderate $t/J$ favors superconductivity from attractive holon interactions.

Abstract

The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or $t$-$J$ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the $d+id$-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t$-$J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of $t/J$, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed.