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

@article{Barbaroux2020GapOI, title={Gap opening in the spectrum of some Dirac-like pseudo-differential operators}, author={Jean-Marie Barbaroux and Horia D. Cornean and Sylvain Zalczer}, journal={arXiv: Mathematical Physics}, year={2020} }

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…

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