Confinement and Fermion Doubling Problem in Dirac-like Hamiltonians

Abstract

We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative $k\to -i{\partial }_x$ skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator Bi${}_2$Se${}_3$, for which we use ab-initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons.

arXiv comment10 pages, 9 figures

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• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice
• Spectral features of magnetic domain walls on surface of 3D topological insulators
• Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers
• Quantum transport through three-dimensional topological insulator p-n junction under magnetic field
• Local Optical Conductivity of Bilayer Graphene with Kink Potential
• Anisotropic transport properties in prismatic topological insulator nanowires
• Resonant helical multi-edge transport in Sierpiński carpets
• Exact lattice-model calculation of boundary modes for Weyl semimetals and graphene
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Massive Dirac states bound to vortices by a boson-fermion interaction