mKdV equation approach to zero energy states of graphene

Abstract

We utilize the relation between soliton solutions of the mKdV and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero energy states of graphene.

4 pages, 4 figures. Abstract and figures improved, references updated

References in corpus (12)

• Electric Field Effect in Atomically Thin Carbon Films
• Chiral tunneling and the Klein paradox in graphene
• Electronic States of Graphene Nanoribbons
• Magnetic confinement of massless Dirac fermions in graphene
• The zero-energy state in graphene in a high magnetic field
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Multiple magnetic barriers in graphene
• Electrostatic confinement of electrons in an integrable graphene quantum dot
• Zero-energy states in corrugated bilayer graphene
• One-dimensional Coulomb problem in Dirac materials
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Bound States in Graphene

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• Dynamics of electrons and explicit solutions of Dirac-Weyl systems
• On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications
• 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
• A systematic construction of parity-time ($\mathcal{P}\mathcal{T}$)-symmetric and non-$\mathcal{P}\mathcal{T}$-symmetric complex potentials from the solutions of various real nonlinear evolution equations
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime