The map between symmetries and orbital rules to realize tunable band gap in quantum anomalous Hall effect material

We establish the map between symmetries and orbital rules to realize tunable band gap in quantum anomalous Hall effect material. The band gap is determined by the spin–orbit coupling between local orbitals associated with band crossings, is constrained by at least one lattice symmetry, and can be turned on/off by breaking or keeping the corresponding lattice symmetry through rotation of the magnetization direction. Local orbital components associated with band crossings need to match the symmetry and produce non-zero spin–orbit coupling when the symmetry is broken. According to this map, TiSb monolayer is predicted to be a quantum anomalous Hall effect material with band gap that can be adjusted in the range of 0 to 209 meV by rotating the magnetization direction. •The map between symmetries and orbital rules to realize tunable band gap was established.•The TiSb monolayer was predicted to be a quantum anomalous Hall effect material.•A tunable band gap of 0∼209 meV was achieved by rotating the magnetization direction.