Kinetic obstruction to pairing in the doped Kitaev-Heisenberg ladder

TL;DR

This study explores how doping affects pairing and magnetic phases in the doped Kitaev-Heisenberg ladder, revealing kinetic energy-dependent pairing tendencies and phase transitions using DMRG simulations.

Contribution

It provides the first detailed analysis of doping effects on the Kitaev-Heisenberg ladder, highlighting the role of kinetic energy in pairing and phase behavior.

Findings

Pairing tendencies occur for t/K less than approximately 0.65.

Doped ladder exhibits superconducting correlations in the rung-singlet phase.

Charge-density-wave correlations dominate at weak doping near the stripy phase transition.

Abstract

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 first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength $t$ and doping level. This reveals intriguing pairing tendencies only for $\frac{t}{K} \lesssim 0.65$, 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 the spatial profiles of the plaquette operator and the charge density. We 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. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.