  We derive the spectra of surface states for massive Dirac Hamiltonians with
either momentum or energy separation between the left- and right-handed Weyl
nodes. Momentum separation between the Weyl nodes corresponds to the explicitly
broken time-reversal symmetry and the energy separation - to broken parity.
Such Hamiltonians provide the simplest model description of Weyl semimetals. We
find that the only effect of the energy separation between the Weyl nodes is to
decrease the Fermi velocity in the linear dispersion relation of the surface
states of massive Dirac Hamiltonian. In the case of broken time-reversal
symmetry, the spectrum of surface states interpolates in a nontrivial way
between the Fermi arc-type and the Dirac cone-type dispersion relations. In
particular we find that for all values of the mass and the momentum separation
between the Weyl nodes the surface states only exist in a strip of finite width
in momentum space. We give also some simpler examples of surface states in
order to make these notes more pedagogical.
