• Corpus ID: 211010856

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}
}

• J. Barbaroux, H. Cornean, S. Zalczer
• Published 2 February 2020
• Mathematics
• arXiv: Mathematical Physics

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.