Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields

We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets. It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from $\pm 1$ to zero. This gapful spin liquid state with zero Chern number is nothing but the toric code phase. Our result potentially explains the topological nematic transition recently observed in $\alpha$-RuCl$_3$ via heat capacity measurements [O. Tanaka et al., arXiv:2007.06757].