Green's function of semi-infinite Weyl semimetals

We classify all possible boundary conditions (BCs) for a Weyl material into two classes: (i) BC that mixes the spin projection but does not change the chirality attribute, and (ii) BC that mixes the chiralities. All BCs are parametrized with angular variables that can be regarded as mixing angles between spins or chiralities. Using the Green's function method, we show that these two BCs faithfully reproduce the Fermi arcs. The parameters are ultimately fixed by the orientation of Fermi arcs. We build on our classification and show that in the presence of a background magnetic field, only the second-type BC gives rise to nontrivial Landau orbitals.