Confining massless Dirac particles in two-dimensional curved space

Abstract

Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.

10 pages 8 figures

References in corpus (38)

• The electronic properties of graphene
• Topological insulators and superconductors
• Dirac semimetal in three dimensions
• Topological States and Adiabatic Pumping in Quasicrystals
• Dirac materials
• Spectroscopic evidence for type II Weyl semimetal state in MoTe2
• The Rare Two-Dimensional Materials with Dirac Cones
• Fermi velocity engineering in graphene by substrate modification
• Space dependent Fermi velocity in strained graphene
• Lattice Boltzmann Equation for Quantum Mechanics
• Electrostatic confinement of electrons in an integrable graphene quantum dot
• Electronic properties of curved graphene sheets
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• The surface states of topological insulators - Dirac fermion in curved two dimensional spaces
• The Hawking-Unruh phenomenon on graphene
• Wave function mapping in graphene quantum dots with soft confinement
• Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain
• Guided modes in graphene waveguides
• Pre-Turbulent Regimes in Graphene Flows
• Relativistic electron wave packets carrying angular momentum
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Bielectron vortices in two-dimensional Dirac semimetals
• Hydrodynamic Model for Conductivity in Graphene
• Quantum walks as massless Dirac Fermions in curved Space-Time
• Colloidal topological insulators
• Bound States in Nanoscale Graphene Quantum Dots in a Continuous Graphene Sheet
• Localization of massless Dirac particles via spatial modulations of the Fermi velocity
• On bound states of Dirac particles in gravitational fields
• A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot
• Conformal Invariance of Graphene Sheets
• Gaussian Quadrature and Lattice Discretization of the Fermi-Dirac Distribution for Graphene
• Chiral interface states in graphene $p$-$n$ junctions
• Excitonic instability in optically-pumped three-dimensional Dirac materials
• Rayleigh-Bénard Instability in Graphene
• Visualizing the kinematics of relativistic wave packets
• Shifted Landau levels in curved graphene sheets
• Klein Tunneling in the presence of random impurities
• Trapping massless Dirac particles in a rotating saddle

Cited by in corpus (14)

• Curvature-induced quantum spin-Hall effect on a Möbius strip
• Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
• Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures
• On the propagation of Dirac fermions in graphene with the strain-induced inhomogeneous Fermi velocity
• Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces
• Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
• AdS/CFT Correspondence with a 3D Black Hole Simulator
• Quantized alternate current on curved graphene
• Tunable Dirac points and zero-energy modes in periodic curved graphene superlattices
• Inverse design of strained graphene surfaces for electron control
• Selective Thermalization, Chiral Excitations, and a Case of Quantum Hair in the Presence of Event Horizons
• Two-dimensional Dirac matter in the semiclassical regime
• Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field
• Landau levels in wrinkled and rippled graphene sheets