Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration

We study the Kitaev model with direction dependent interactions to investigate how the flux configuration and/or the anisotropy in the exchanges affect the Majorana excitations. Systematic numerical calculations demonstrate how the anisotropy of the exchange couplings and flux configuration make the Majorana excitation gapped. The induced gapped quantum spin liquid states are distinct from the gapped one realized in the large anisotropic limit. The nature of gapped states can be explained by the superlattice potential due to flux configuration.