Phase diagrams of Weyl semimetals with competing diagonal and off-diagonal disorders

A Weyl semimetal (WSM) is a topological material that hosts Weyl fermions as quasiparticles in the bulk. We study the effects of diagonal and off-diagonal disorders on WSMs by adopting a tight-binding model that supports the WSM, the three-dimensional quantum anomalous Hall (3D QAH) and the normal insulator (NI) phases in the clean limit. Basing on the calculation of the localization length and the Hall conductivity, we present rich phase diagrams when WSMs are subject to the two types of disorders. We find that the WSM with well-separated Weyl nodes is stable against weak disorder. Weak diagonal disorder may annihilate the Weyl nodes in the WSM phase close to the 3D QAH phase, resulting in a 3D QAH state, and it could also create Weyl nodes in the NI phase near the WSM phase, leading to a WSM. Reversely, weak off-diagonal disorder may nucleate Weyl nodes in the 3D QAH phase in proximity to the WSM phase, causing a 3D QAH-WSM transition, or it could destroy Weyl nodes in the WSM phase near the NI phase, bringing about a WSM-NI transition. We observe a diffusive anomalous Hall metal (DAHM) phase at moderate disorder strength. The DAHM appears in a wide range of the phase diagram when the diagonal disorder dominates over the off-diagonal disorder, while the DAHM is found to exist in a narrow region or be missing in the phase diagram when the off-diagonal disorder dominates.