Gap opening in the spectrum of some Dirac-like pseudo-differential operators

2020/02/02 by Jean-Marie Barbaroux, Barbaroux, J. -M., Horia D. Cornean +3
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Algebraic and Geometric Analysis #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2002.00422

Abstract

In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by σ⋅ F(-i∇), where σ denotes the Pauli matrices and F is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on F, and we study how this gap depends on different parameters.

Citations

• The electronic properties of graphene

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