Geometry-independent tight-binding method for massless Dirac fermions in two dimensions

The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for the naive discretization of single (massless) Dirac cone on two-dimensional surface. inevitable appearance an additional, unphysical fermionic mode can, example, be circumvented by introducing extra dimension to spatially separate cones. In this work, we propose geometry-independent protocol based tight-binding model three-dimensional topological insulator cubic lattice. low-energy theory, below bulk gap, corresponds its surface which can have arbitrary geometry. We introduce method where only thin shell needs simulated. Depending setup, gap out states undesired surfaces either breaking time-reversal symmetry or superconducting pairing. show that it is enough thickness topological-insulator three nine lattice constants. This leads effectively scaling with minimal and fixed thickness. test idea comparing spectrum probability distribution analytical results both proximitized sphere exhibits nontrivial spin-connection. yields simulating cones small overhead due finite shell.