Zero Modes and Charged Skyrmions in Graphene Bilayer

We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers's theorem implied by the "pseudo time reversal'' symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.