Nonlocal spin correlation as a signature of Ising anyons trapped in vacancies of the non-Abelian Kitaev spin liquid

Determining the elementary excitations in α-RuCl3 under in-plane magnetic fields over 7T is the foremost challenge in Kitaev spin liquid research. While the thermal Hall conductance plateau observed in some experimental groups may be consistent with Kitaev's prediction for the chiral spin liquid phase, the origin of such conductance is still under debate. To conclusively confirm the existence of the non-Abelian Kitaev spin liquid in this candidate material, a direct probe of Ising anyons within the bulk is indispensable. This theoretical study aims to elucidate how nonlocal correlations of Ising anyons become discernible in observables [arXiv:2211.13884]. By constructing an analytical formula for nonlocal spin correlations between spin sites, each of which is adjacent to two isolated vacancies, we confirm that the nonlocality of Ising anyons manifests in specific long-range spin correlations within the spin liquid backgrounds. We also discover that the dynamical nonlocal spin correlation function is electrically detectable through the observation of nonzero nonlocal conductance in the Kitaev magnet/metallic substrate heterostructure. Our proposed setup can be employed to directly probe vacancy-trapped Ising anyons, thus confirming the existence of the Kitaev chiral spin liquid in α-RuCl3.