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

Jean-Marie Barbaroux (1, 2) , H D Cornean , S Zalczer (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E8 Dynamique quantique et analyse spectrale

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.

Domaines: Physique mathématique [math-ph]

Jean-Marie Barbaroux, H D Cornean, S Zalczer. Gap opening in the spectrum of some Dirac-like pseudo-differential operators. Revue roumaine de mathématiques pures et appliquées, 2021, 66 (3-4), pp.597-616. ⟨hal-02463983⟩