Title: Efficient semiclassical approximation for bound states in graphene in magnetic field with a small trigonal warping correction

Abstract: This paper is devoted to the construction of efficient (simple to implement) explicit semiclassical asymptotic eigenfunctions of the Dirac operator for high-energy bound states in graphene in magnetic field. When considering excited states in graphene, a distortion called trigonal warping begins to play an~important role, see [7], [12]. We are dealing with a~trigonal warping correction, considering it to be small. While the standard semiclassical methods allow one to solve the eigenequations for operators if and only if quantization conditions are met, we, based on article [1], develop approaches that can be used in case these conditions are violated. The complete symbol turns out to be only close to integrable, which brings its own difficulties. The present paper relies heavily on the results from [3].