Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

Abstract

We study the extended Kitaev model called the KΓ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in α-RuCl3, even for sufficiently small values of Γ/|K|. The latter has a Majorana zero mode in its Z3 vortex core, which can be potentially controlled by the domain wall motion. This opens a possible application of the quantum liquid crystal phases in the KΓ model to the topological quantum computation.

Phase Diagrams of Kitaev Models for Arbitrary Magnetic-Field Orientations

“…[63] has addressed this issue and also the magnetic field effects perturbatively, yet assuming a KSL GS. In this respect, it is crucial to clarify the effect of large Γ ∼ |K| [64,65] as well as arbitrary magnetic field orientations and strengths to understand the validity of existing results based on the putative F Kitaev GS. Naturally, an unbiased method is needed where the ordered phases and the fractional phases are treated on equal footing.…”