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.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.

arXiv:2608.03024Aug 4, 20260 citations

Coupling of Two Superconductors through a Ferromagnet

J. Aarts, A. A. Golubov, V. A. Oboznov +3 more

Jan 1, 2001601 citations

Superfluidity and superconductivity

C. Di Castro, Roberto Raimondi

Cambridge University Press eBooksAug 27, 20154 citations

Coexistence of strong pairing correlations and itinerant ferromagnetism arising from spin asymmetric bandwidths: A reduced BCS model study

Zu‐Jian Ying, Mario Cuoco, Canio Noce +1 more

We investigate the conditions for the occurrence of the coexisting phases that exhibit singlet superconductivity and itinerant ferromagnetism arising from spin asymmetric bandwidths. The exact solution for a reduced BCS pairing model with spin dependent bandwidths is used to determine the ground-state diagram as a function of the coupling parameter, the total density, and the topology of the single-particle spectrum. A spin-polarized superconducting state is obtained in the regime of large pair couplings with a strong bandwidth asymmetry. The analysis reveals that, for such a type of ferromagnetism, small (large) values of the density of states at energies close to the edges of the band enhance (hinder) the tendency toward a coexistence of strong pairing correlations and finite spin polarizations.We investigate the conditions for the occurrence of the coexisting phases that exhibit singlet superconductivity and itinerant ferromagnetism arising from spin asymmetric bandwidths. The exact solution for a reduced BCS pairing model with spin dependent bandwidths is used to determine the ground-state diagram as a function of the coupling parameter, the total density, and the topology of the single-particle spectrum. A spin-polarized superconducting state is obtained in the regime of large pair couplings with a strong bandwidth asymmetry. The analysis reveals that, for such a type of ferromagnetism, small (large) values of the density of states at energies close to the edges of the band enhance (hinder) the tendency toward a coexistence of strong pairing correlations and finite spin polarizations.

Physical Review BSep 23, 200815 citations

Coexistence of Spin-Triplet Superconductivity with Antiferromagnetism in Orbitally Degenerate System: Hartree-Fock Approximation

M. Zegrodnik, Józef Spałek

We consider the coexistence of the Hund's-rule-exchange induced spin-triplet paired state with the antiferromagnetic ordering by starting from the extended Hubbard model for a doubly degenerate band.We use the density of states appropriate for the square lattice and treat the problem in the HartreeFock approximation.The temperature dependences of the superconducting gaps, the magnetic moment, and the chemical potential are presented.The free energy in the considered phase is evaluated, as well as the corresponding free energies in four additional phases: paramagnetic, ferromagnetic, superconducting of type A and superconducting of type A1 coexisting with ferromagnetism; they occur in the proper range of parameters: band lling n and the interaction parameters U/W and J/W .The low temperature values of the superconducting gaps and staggered magnetic moment are also analyzed as a function of band lling.We consider the coexistence of the Hund's-rule-exchange induced spin-triplet paired state with the antiferromagnetic ordering by starting from the extended Hubbard model for a doubly degenerate band.We use the density of states appropriate for the square lattice and treat the problem in the HartreeFock approximation.The temperature dependences of the superconducting gaps, the magnetic moment, and the chemical potential are presented.The free energy in the considered phase is evaluated, as well as the corresponding free energies in four additional phases: paramagnetic, ferromagnetic, superconducting of type A and superconducting of type A1 coexisting with ferromagnetism; they occur in the proper range of parameters: band lling n and the interaction parameters U/W and J/W .The low temperature values of the superconducting gaps and staggered magnetic moment are also analyzed as a function of band lling.

Acta Physica Polonica AApr 1, 20122 citations

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.