Electronic properties of bilayer graphene catenoid bridge

Abstract

We study the properties of an electron on a catenoid surface. The catenoid is understood as a realization of a bridge connecting two graphene layer by a smooth surface. The curvature induces a symmetrical reflectionless potential well around the bridge with one bound-state for $m=0$. For $m\ne 0$, a centrifugal potential barrier arises controlling the tunnelling between the layers. An external electric field breaks the parity symmetry and provides a barrier that controls the conductance from one layer to another. By applying a constant magnetic field the effective potential exhibits a confining double-well potential nearby the bridge. We obtain the corresponding bound states and study the effects of the curvature on the Landau levels.

arXiv comment7 figures

References in corpus (22)

• The electronic properties of graphene
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Unusually High Thermal Conductivity of Carbon Nanotubes
• Making Sense of Non-Hermitian Hamiltonians
• Generating quantizing pseudomagnetic fields by bending graphene ribbons
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Geometric Phases in Graphitic Cones
• Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
• Tuning electronic properties of corrugated graphene: confinement, curvature and band gap opening
• Möbius Graphene Strip as Topological Insulator
• Geometry induced charge separation on a helicoidal ribbon
• Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Geometry induced potential on a 2D-section of a wormhole: catenoid
• Helicoidal Graphene Nanoribbons: Chiraltronics
• Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential
• Quantum Hall-like effect on strips due to geometry
• Quantum anticentrifugal force for wormhole geometry
• Dual oscillators and Quantum Pendulums: spectrum and correlators
• The chiral massive fermions in the graphitic wormhole

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• Coupled fermion-antifermion pairs within a traversable wormhole
• Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields
• Quantum Holonomies in Graphene Wormholes
• Encoding quantum bits in bound electronic states of a graphene nanotorus
• On quantum traversability of wormholes
• Redshift as a stretching factor in rotating graphene wormholes
• Quantum particle on a surface: Catenary surface and Paraboloid of revolution
• Electronic states in quantum wires on a Möbius strip