Pairing tendencies in the doped Kitaev-Heisenberg model

TL;DR

This study explores how hole doping affects pairing tendencies in the Kitaev-Heisenberg model on a honeycomb lattice, revealing pairing mainly in the Néel phase and signs of pair-density wave formation, with implications for quantum materials.

Contribution

It provides a detailed DMRG analysis of doping effects, highlighting the importance of kinetic energy and revealing pairing and pair-density wave tendencies in the doped Kitaev-Heisenberg model.

Findings

Pairing occurs mainly in the Néel phase at intermediate hopping.

Signatures of pair-density wave formation are observed.

Pairing is suppressed in the pure Kitaev spin-liquid phase.

Abstract

We study the impact of hole-doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a $t-J-K$ model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the N\'eel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.