Quantum liquid crystals in the finite-field K$\Gamma$ model for $\alpha$-RuCl${}_3$

Abstract

We study the extended Kitaev model called the K$\Gamma$ 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 $\alpha$-RuCl${}_3$, even for sufficiently small values of $\Gamma /|K|$. The latter has a Majorana zero mode in its $Z_3$ 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 K$\Gamma$ model to the topological quantum computation.

arXiv comment6 + 3 pages, 4 + 4 figures