Doping the Kitaev-Heisenberg ladder

We study the effects of hole-doping the Kitaev-Heisenberg (t-J-K) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first investigate the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength t and doping. This reveals pairing tendencies only for t≤0.65K, consistent with our prior results on three-leg ladders [Phys. Rev. B 110, 224518 (2024)], and indicating a strong dependence on the kinetic energy of dopants in Kitaev spin liquids. Analysis of one- and two-hole doping in the AFK regime shows that increasing hopping strength results in enhanced spin correlations and decay of the average plaquette operator.

We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions (J≥0) and intermediate hopping t=1. Upon doping, the rung-singlet region develops dominant superconducting correlations, accompanied by competing charge-density correlations and exponentially decaying spin-spin correlations. Charge-density-wave correlations become dominant at higher doping levels, including near the AFK limit. In contrast, spin-density wave-like behavior is found at lower doping at the AFK point, and for all studied doping levels in the ferromagnetic Kitaev limit and the stripe phase.