Discrete Spectrum of the Bilayer Graphene Operator

We consider the graphene operator $D_m$ perturbed by a decaying potential $αV$, where $α$ is a coupling constant. We study the number $N(λ,α)$ of eigenvalues of the operator $D(t)=D_m-tV$ passing through a regular point $λ\inρ(D_m)$ as $t$ changes from $0$ to $α$. We obtain asymptotic formulas for $N(λ,α)$ as $α\to\infty$.