Jean-Claude Cuenin: Eigenvalue Estimates for Bilayer Graphene  

Recently, Ferrulli-Laptev-Safronov proved eigenvalue estimates for an operator associated to bilayer graphene in terms of \(L^q\) norms of the (possibly non-selfadjoint) potential. They proved that for 1 < q < 4/3 all non-embedded eigenvalues lie near the edges of the spectrum of the free operator. In this note we prove this for the larger range 1 ≤ q ≤ 3/2. The latter is optimal if embedded eigenvalues are also considered.
We prove similar estimates for a modified bilayer operator with so-called “trigonal warping” term. Here, the range for q is smaller since the Fermi surface has less curvature.