Dirac-Weyl equation on a hyperbolic graphene surface under magnetic fields

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Kizilirmak D. D., KURU Ş., Negro J.

PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, vol.118, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 118
  • Publication Date: 2020
  • Doi Number: 10.1016/j.physe.2019.113926
  • Journal Name: PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC
  • Keywords: Factorization method, Dirac-Weyl equation, Curved space, Magnetic field, ELECTRONIC-PROPERTIES, CHARGED-PARTICLE, STATES, PLANE
  • Ankara University Affiliated: Yes

Abstract

In this paper the Dirac-Weyl equation on a hyperbolic surface of graphene under magnetic fields is considered. In order to solve this equation analytically for some cases, we will deal with vector potentials symmetric under rotations around the z axis. Instead of using tetrads we will get this equation from a more intuitive point of view by restriction from the Dirac-Weyl equation of an ambient space. The eigenvalues and corresponding eigen-functions for some magnetic fields are found by means of the factorization method. The existence of a zero energy ground level and its degeneracy is also analysed in relation to the Aharonov-Casher theorem valid for flat graphene.