Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with ${Z}₂$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the ${Z}₂$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.