Quasi-exact solution to the Dirac equation for the hyperbolic secant potential

Abstract

We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.

8 pages, 4 figures. Figure 2 removed, 2 additional figures and references added

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• Tunable plasmonic reflection by bound 1D electron states in a 2D Dirac metal
• Bound states in a hyperbolic asymmetric double-well
• Qualitative analysis of trapped Dirac fermions in graphene
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• Semi-exact solutions of the Razavy potential
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• New solutions for graphene with scalar potentials by means of generalized intertwining
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• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• mKdV equation approach to zero energy states of graphene
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• Trapping charge carriers in low-dimensional Dirac materials
• Zero Energy States for a Class of Two-Dimensional Potentials in Graphene
• Generalized harmonic confinement of massless Dirac fermions in (2+ 1) dimensions
• Dynamics of electrons and explicit solutions of Dirac-Weyl systems
• Klein Bound States in Single-Layer Graphene
• Perfectly Conducting Graphene Electronic Waveguide with Curved Channels
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• Dirac equation with complex potentials
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• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Coherent Transport in Y-Junction Graphene Waveguide
• Continuous and discrete dynamical Schrödinger systems: explicit solutions
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Ballistic guided electrons against disorder in graphene nanoribbons
• On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• The violation of a uniqueness theorem and an invariant in the application of Poincaré--Perron theorem to Heun's equation
• Designer gapped and tilted Dirac cones in lateral graphene superlattices
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime