  In a tight-binding model of AA-stacked bilayer graphene, it is demonstrated that a bound defect state within the region of continuous spectrum can exist stably with respect to variations in the strength of a perpendicular magnetic field. This is accomplished by creating a defect that is compatible with the interlayer coupling, thereby shielding the bound state from the effects of the continuous spectrum, which varies erratically in a pattern known as the Hofstadter butterfly. 
Stable defect states in the continuous spectrum of bilayer graphene with   magnetic field