Superconductivity and competing orders in honeycomb $t$-$J$ model: interplay of lattice geometry and next-nearest-neighbor hopping

Abstract

We investigate the extended $t$-$J$ model on honeycomb lattices with next-nearest-neighbor (NNN) electron hopping $t'$ and superexchange coupling $J'=(t'/t)^2 J$ using large-scale density-matrix renormalization group (DMRG) simulations and slave-boson mean-field theory (SBMFT). By systematically varying $t'$ and cylinder geometries, our DMRG results reveal several competing phases with distinct charge and superconducting (SC) properties. On YC4-0 cylinders possessing bonds lying along $\vec{e}_y$ direction, the ground state of doped models exhibits pronounced quasi-long-range $d$-wave SC with coexisting armchair-oriented stripes (a-stripe) across a broad range of $t'$. Notably, the SC Luttinger exponent has a non-monotonic dependence on $t'$, showing an optimal $t'_{op}\sim0.4$ for dominant SC. Conversely, XC cylinders host a competing long-range zigzag stripes phase without SC for $t'>0.5$, highlighting the role of boundary geometry in stabilizing distinct competing phases in DMRG. To elucidate the stability of all these competing phases in 2D limit, we employ SBMFT and identify the a-stripe as the stable configuration across most of phase diagram, with a transition to uniform nematic $d$-wave SC at large $t'$ for $\delta=1/8$. The combined results from two complementary approaches suggest a robust $t'$-induced SC phase that might remain stable in doped extended $t$-$J$ model on the honeycomb lattice.