Magic radius of an AA -stacked bilayer graphene quantum dot

We study analytically and numerically electronic properties of a circular quantum dot made from AA-stacked bilayer graphene. We observe a discrete set of dot radii for which the low-energy electron states are degenerate with respect to the layer parity. By analogy with the ``magic angles'' in the twisted bilayer graphene we refer to these radii as ``magic.'' Such a feature is unique for the AA structures and is related to a specific layer symmetry of the AA graphene bilayer: the parity of the highest occupied level changes from layer-symmetric to layer antisymmetric when the radius of the AA dot is equal to its magic value. We explore an analogy in the electronic structure between twisted bilayer graphene at the magic twist angle and the AA quantum dot with magic radius. We argue that this analogy can be helpful for theoretical description of the electronic properties of the twisted bilayer graphene.