Confinement and Fermion Doubling Problem in Dirac-like Hamiltonians

*We investigate the interplay between confinement and the Fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. Firstly, simple electrostatic gates do not confine electrons due to the Klein tunneling. Secondly, typical lattice discretization of the first order derivative* $$k\mapsto−i\partial x$$ *skips the central point and allow spurious low-energy, highly oscillating solutions known as the 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 calculating the band structure and transport properties across thin films of the topological insulator $$Bi_2Se_3$$, for which we use ab-initio DFT calculations to justify the model.*