Topological and magnetic phase transitions in bilayer Kitaev-Ising model*

We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising inter-layer interactions via Majorana mean field theory and perturbative analysis. We show that a diverse array of magnetic and topological phase transitions occur with inter-layer exchange depending on the direction of the Ising interaction and the relative sign of the Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin-liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite sign of the Kitaev interaction, we observe a notable weakening of the magnetic tendencies and the Kitaev spin liquid survives up to a remarkably larger inter-layer exchange. Our analysis identifies the emergence of an intermediate gapped Ζ₂ spin liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120° compass model. We conclude with a discussion on the perturbative analysis when the Ising axis lie along z-axis or in the xy-plane. In both cases, our analysis reveals the formation of 1D Ising chains, which intriguingly remain decoupled up to the sixth order in perturbation theory. Our results highlight the interplay between topological order and magnetic tendencies in bilayer quantum spin liquids.