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arXiv:2608.03024

Exotic superconductivity in the doped Kitaev quantum spin liquid

Takahiro Misawa, Kota Ido

Published Aug 4, 2026• 0 citations
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Abstract

We investigate superconductivity in a doped Kitaev quantum spin liquid by applying the many-variable variational Monte Carlo method to the hole-doped $t$-$J$-type Kitaev model. Using a projected pair-product wave function that can exactly represent the Kitaev quantum spin liquid, we examine the stability of superconducting phases on isotropic two-dimensional clusters. For the ferromagnetic Kitaev interaction, robust triplet $p$-wave superconductivity coexists with ferromagnetism in the low-to-intermediate doping regime but is suppressed as the system approaches the fully polarized ferromagnetic phase. For the antiferromagnetic Kitaev interaction, superconductivity exhibits a change in the dominant pairing symmetry from spin-dependent triplet $p$-wave at low doping to singlet $d+id$ at intermediate doping. By varying the strength of the ferromagnetic Kitaev interaction at fixed doping, we show that the triplet superconductivity increases together with the ferromagnetic moment and becomes strongest slightly below full polarization. Our results provide a theoretical basis for experimental searches for unconventional superconductivity, such as triplet superconductivity coexisting with ferromagnetism, in carrier-doped Kitaev candidate materials.

DOI
10.48550/arxiv.2608.03024

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We investigate superconductivity in a doped Kitaev quantum spin liquid by applying the many-variable variational Monte Carlo method to the hole-doped ttt-JJJ-type Kitaev model. Using a projected pair-product wave function that can exactly represent the Kitaev quantum spin liquid, we examine the stability of superconducting phases on isotropic two-dimensional clusters. For the ferromagnetic Kitaev interaction, robust triplet ppp-wave superconductivity coexists with ferromagnetism in the low-to-intermediate doping regime but is suppressed as the system approaches the fully polarized ferromagnetic phase. For the antiferromagnetic Kitaev interaction, superconductivity exhibits a change in the dominant pairing symmetry from spin-dependent triplet ppp-wave at low doping to singlet d+idd+idd+id at intermediate doping. By varying the strength of the ferromagnetic Kitaev interaction at fixed doping, we show that the triplet superconductivity increases together with the ferromagnetic moment and becomes strongest slightly below full polarization. Our results provide a theoretical basis for experimental searches for unconventional superconductivity, such as triplet superconductivity coexisting with ferromagnetism, in carrier-doped Kitaev candidate materials.
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 tK≲0.65\frac{t}{K}\lesssim 0.65Kt​≲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.
We investigate the hole-doped Kitaev-Heisenberg (ttt-JJJ-KKK) 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 ttt and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K} \lesssim 0.65Kt​≲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=1t=1t=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.
Motivated by exploring correlated metals with frustrating bond-dependent exchange interactions, we study hole and electron doped Kitaev Mott insulators on the triangular lattice. Using homogeneous parton mean field theory, we find that the stripe antiferromagnetic (AFM) order for Kitaev coupling K>0K>0K>0 and the ferromagnetic (FM) order for K<0K<0K<0, both vanish at sufficiently large doping, beyond which we find regimes with chiral d±idd\pm i dd±id singlet pairing and p±ipp\pm ipp±ip triplet pairing respectively. Our tensor network computations however reveal that the superconducting correlations are strongly suppressed; while FM order stubbornly persists for the doped K<0K<0K<0 model, the doped K>0K>0K>0 model features emergent spin-charge modulated stripe orders. At higher hole doping for K>0K > 0K>0, where AFM order is more strongly suppressed than for the electron doped case, incorporating a sufficiently strong nearest-neighbor attraction yields evidence for singlet ddd-wave superconductivity with Luttinger parameter Ksc<1K_{\rm sc} < 1Ksc​<1. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as NaRuO2_22​ which feature bond-dependent exchange interactions.
We study the hole-doped Kitaev-Heisenberg chain using the density-matrix renormalization group. In the Kitaev-only limit, the bond-directional exchange itself promotes pairing, favoring spin-singlet and spin-triplet superconducting tendencies for antiferromagnetic and ferromagnetic Kitaev couplings, respectively, together with finite-size Majorana edge correlations suggestive of topological superconductivity. In the full Kitaev-Heisenberg chain, cooperative J - and K exchanges broadly stabilize superconductivity, while competition between J and K induces a strong filling dependence and enables superconductivity even when both J and K are weak. At quarter filling, this competition produces a Mott insulator with spontaneous hopping dimerization. These results identify magnetic frustration as a common mechanism underlying superconducting and interaction-driven insulating phases in doped Kitaev systems.
The possible ground states of the undoped and doped Kitaev–Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases, including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated using the Schwinger-fermion mean-field method, and we obtain an energetically favorable Z 2 chiral spin liquid with a Chern number ±2 as a promising candidate. At finite doping, we find that the AF Heisenberg coupling supports an s -wave or a -wave superconductivity (SC), while the AF and the ferromagnetic Kitaev interactions favor a -wave SC and a time-reversal invariant topological p -wave SC, respectively. Possible experimental realizations and related candidate materials are also discussed.
We study the quantum many-body instabilities of the t−JK−JHt -J_{\mathrm{K}} - J_{\mathrm{H}}t−JK​−JH​ Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-1/21/21/2 model is believed to describe the magnetic properties of the layered transition-metal oxide Na2_22​IrO3_33​. We determine the ground-state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow-equations adapted to the lack of full spin-rotational invariance in the fermionic interactions, here represented by the highly frustrated and anisotropic Kitaev exchange term. Additionally employing a set of Ward identities for the Kitaev-Heisenberg model, the numerical solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold (Z2\mathbb{Z}_2Z2​ quantum spin liquids and magnetically ordered phases). We corroborate superconducting triplet ppp-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. For filling δ>1/4δ> 1/4δ>1/4, the ppp-wave pairing gives rise to a topological state with protected Majorana edge-modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchange we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice. Further, our flow equations are applicable to a wider class of model Hamiltonians.