Agradecimentos: The authors thank the colleagues of the Universidade Estadual de Campinas, specially Pascoal Pagliuso and Yakov Kopelevich, for useful discussions. The authors also thank the colleagues involved in the MultiSuper International Network (http://www.multisuper.org) for exchange of ideas and suggestions for this work. AP acknowledges support by the University of Camerino FAR project CESEMN Ver menos

Abstract: Weyl fermions are shown to exist inside a parabolic band in a single electronic layer, where the kinetic energy of carriers is given by the non-relativistic Schroedinger equation. There are Fermi arcs as a direct consequence of the folding of a ring-shaped Fermi surface inside the first Brillouin zone. Our results stem from the decomposition of the kinetic energy into the sum of the square of the Weyl state, the coupling to the local magnetic field and the Rashba interaction. The Weyl fermions break the space and time reflection symmetries present in the kinetic energy, thus allowing for the onset of a weak three-dimensional magnetic field around the layer. This field brings topological stability to the current-carrying states through a Chern number. In the special limit for which the Weyl state becomes gapless, this magnetic interaction is shown to be purely attractive, thus suggesting the onset of a superconducting condensate of zero helicity states Ver menos