Kinetic obstruction to pairing in the doped Kitaev-Heisenberg two-leg ladder

Abstract Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg ( t – J – K ) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for $$\frac{t}{K}\lesssim 0.65$$ t K ≲ 0.65 , consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase.