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

TL;DR

This paper investigates the K$ extGamma$ model relevant to $ extalpha$-RuCl$_3$, revealing new quantum liquid crystal phases, including nematic and Kekulé Kitaev spin liquids, with potential implications for topological quantum computing.

Contribution

It introduces the discovery of nematic and Kekulé Kitaev spin liquids in the K$ extGamma$ model, linking them to experimental observations and topological quantum computation.

Findings

Identification of a nematic Kitaev spin liquid phase.

Discovery of a Kekulé Kitaev spin liquid with Majorana zero modes.

Potential control of quantum states via domain wall motion.

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 Kekul\'e 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.