Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields

Abstract

The present article discusses magnetic confinement of the Dirac excitations in graphene in presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to $1/r$ is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in presence of the $1/r$ (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cut-off Coulomb potential to dictate the excitation spectra of the states of graphene. The spectrum of the graphene excitations in presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.

9 pages, 6 figures, to appear in Journal of Physics: Condensed Matter

References in corpus (9)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Magnetic confinement of massless Dirac fermions in graphene
• Quantum dots in graphene
• Quasi-bound states of quantum dots in single and bilayer graphene
• Multiple magnetic barriers in graphene
• Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes
• Quasi-bound states of Schrodinger and Dirac electrons in magnetic quantum dot

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• Zero-energy vortices in Dirac materials
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Trapping charge carriers in low-dimensional Dirac materials
• Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide
• Theory of magnetotransport in shaped topological insulator nanowires
• Coherent states in the symmetric gauge for graphene under a constant perpendicular magnetic field
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime