Eigenvalue Estimates for Bilayer Graphene
Spectral Methods in Mathematical Physics
02 April 15:30 - 16:30
Jean-Claude Cuenin - LMU Ludwig-Maximilians-Universität München
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.
University of Zurich, UZH