Zero-energy vortices in Dirac materials

Abstract

In this brief review, we survey the problem of electrostatic confinement of massless Dirac particles, via a number of exactly solvable one- and two-body models. By considering bound states at zero energy, we present a route to obtain truly discrete states of massless Dirac particles in scalar potentials, circumventing the celebrated Klein tunnelling phenomenon. We also show how the coupling of two ultrarelativistic particles can arise, and discuss its implications for cutting-edge experiments with two-dimensional Dirac materials. Finally, we report an analytic solution of the two-body Dirac-Kepler problem, which may be envisaged to bring about a deeper understanding of critical charge and atomic collapse in mesoscopic Dirac systems.

11 pages, 1 figure

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Cited by in corpus (12)

• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• Klein Bound States in Single-Layer Graphene
• Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• Bound electron pairs formed by the spin-orbit interaction in 2D gated structures
• Radiative Decay of Bound Electron Pairs in Two-Dimensional Topological Insulators
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• SUSY design of smooth quantum rings in graphene
• Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point
• 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