A quantum spin liquid is a state of matter in which the magnetic moments of atoms behave like a fluid: they constantly fluctuate and never settle into a rigid order, even at extremely low temperatures. One of the most famous theoretical models of such a liquid was proposed by Alexei Kitaev. It describes particles on a hexagonal lattice interacting in a special way — via the so-called Kitaev exchange.

In the new study, the authors added free charges (holes) to this model and investigated whether superconductivity could emerge. Using a powerful computational method, they found that it indeed can. Moreover, the type of superconductivity depends on the nature of the magnetic interaction. If the interaction is ferromagnetic, where magnetic moments tend to align in the same direction, then at moderate hole doping, triplet superconductivity appears. In this state, electron pairs carry spin 1. Such superconductivity stubbornly coexists with ferromagnetism but vanishes when the material becomes fully magnetized.

If the interaction is antiferromagnetic, neighboring magnetic moments prefer to be antiparallel, the picture becomes more complex. At low hole doping, triplet superconductivity still dominates, but as the doping increases, singlet superconductivity with d+id symmetry takes over. This smooth crossover between two pairing types is a rare and intriguing phenomenon.

The authors also showed that triplet superconductivity strengthens as magnetization grows, peaking just before full magnetic saturation. This provides a clear guide for experiments: unconventional superconductivity should be sought in lightly doped Kitaev materials that are on the verge of magnetic ordering.