Gutzwiller approximation approach to the SU(4) $t$-$J$ model

TL;DR

This paper develops a Gutzwiller approximation for the SU(4) $t$-$J$ model, revealing that extended s-wave superconductivity is favored near quarter filling and that spin-singlet and triplet pairings can coexist, with implications for twisted bilayer graphene.

Contribution

It introduces a Gutzwiller approximation for the SU(4) $t$-$J$ model and analyzes its superconducting states on a honeycomb lattice, highlighting coexistence of pairing types.

Findings

Extended s-wave superconductivity is more favorable than d+id near quarter filling.

Spin-singlet and triplet pairings can coexist in the SU(4) model.

Results offer insights into twisted bilayer graphene systems.

Abstract

We develop the Gutzwiller approximation method to obtain the renormalized Hamiltonian of the SU(4) $t$-$J$ model with the corresponding renormalization factors. Subsequently, a mean-field theory is employed on the renormalized Hamiltonian of the model on the honeycomb lattice under the scenario of a cooperative condensation of carriers moving in the resonating valence bond state of flavors. In particular, we find that the extended $s$-wave superconducting state is more favorable than the $d\pm id$-wave superconducting state in the doping range close to quarter filling. The pairing states of the SU(4) case reveal the property that the spin-singlet pairing and the spin-triplet pairing can coexist simultaneously. Our results might provide new insights into the twisted bilayer graphene system.