Correlated topological states and phase diagram of doped Kitaev materials under strong magnetic fields

Motivated by recent experiments on proximately coupled graphene and α-RuCl₃, we theoretically investigate the global phase diagram of a slightly doped Kitaev spin liquid under a strong magnetic field vertical to the lattice plane. This system can potentially realize strongly correlated topological states with exotic anyon contents, where the fractional quantum Hall fluids coexist with the magnetically stabilized chiral spin liquid. Performing variational Monte Carlo calculations combined with effective topological field theory descriptions, we find multiple Abelian and non-Abelian topological phases. We also discuss how these states can be accessed and detected in experiments.