Zero Energy States for a Class of Two-Dimensional Potentials in Graphene

Abstract

The excitations in graphene and some other materials are described by two-dimensional massless Dirac equation with applied external potential of some kind. Solutions of this zero energy equation are built analytically for a wide class of scalar potentials. In contrast to most publications on analytical solutions of massless two-dimensional Dirac equation, our potentials really depend on both spatial coordinates in some bounded domain. Several examples of such construction are given explicitly.

9 pages

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Cited by in corpus (7)

• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Zero-energy vortices in Dirac materials
• New solutions for graphene with scalar potentials by means of generalized intertwining
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime