Here we study the instabilities of a quadratic band crossing system to Chern insulating states and uncorrelated disorder. We determine the phase diagram in the plane of topological mass versus disorder strength, characterizing the system with respect to the spectral, localization, and topological properties. In the clean limit, the system has two gapped Chern insulating phases with Chern numbers $C=\pm 2$ and a trivial phase with $C=0$. For finite disorder, the quadratic band crossing points are unstable to emergent gapless Chern insulating phases with $C=\pm 1$ that are not present in the clean limit. These phases occupy a considerable region of the phase diagram for intermediate disorder and show features of topological Anderson insulators: it is possible to reach them through disorder-driven transitions from trivial phases.

• Received 24 January 2024
• Revised 12 April 2024
• Accepted 30 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184206