Construction of zero energy states in graphene through the supersymmetry formalism

Abstract

We devise a supersymmetry-based method for the construction of zero-energy states in graphene. Our method is applied to a two-dimensional massless Dirac equation with a hyperbolic scalar potential. We determine supersymmetric partners of our initial system and derive a reality condition for the transformed potential. The Dirac potentials generated by our method can be used to approximate interactions that are experimentally realizable.

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Cited by in corpus (11)

• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Bilayer graphene in periodic and quasiperiodic magnetic superlattices
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• SUSY design of smooth quantum rings in graphene
• 2N-Dimensional Canonical Systems and Applications
• Confinement in bilayer graphene via intra- and inter-layer interactions
• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators