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.

References in corpus (21)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Supersymmetry and Quantum Mechanics
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Magnetic confinement of massless Dirac fermions in graphene
• The zero-energy state in graphene in a high magnetic field
• The Electronic Spectrum of Fullerenes from the Dirac Equation
• Multiple magnetic barriers in graphene
• Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
• Supersymmetric Quantum Mechanics
• Quasi-bound states of Schrodinger and Dirac electrons in magnetic quantum dot
• One-dimensional Coulomb problem in Dirac materials
• Searching for confined modes in graphene channels: the variable phase method
• Kronig-Penney model on bilayer graphene: spectrum and transmission periodic in the strength of the barriers
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Qualitative analysis of trapped Dirac fermions in graphene
• Magnetic ratchet effect in bilayer graphene
• On zero energy states in graphene
• Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings
• An analysis of the zero energy states in graphene
• Charge-density-wave states in double-layer graphene structures in a high magnetic field

Cited by in corpus (17)

• Trends in supersymmetric quantum mechanics
• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• New solutions for graphene with scalar potentials by means of generalized intertwining
• Zero Energy States for a Class of Two-Dimensional Potentials in Graphene
• 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
• Two-dimensional Dirac fermion in presence of an asymmetric vector potential
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• Qualitative analysis of magnetic waveguides for two-dimensional Dirac fermions
• 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
• SUSY design of smooth quantum rings in graphene
• The massless Dirac-Weyl equation with deformed extended complex potentials
• 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