Magnetic description of the Fermi arc in type-I and type-II Weyl semimetals

We consider finite-sized interfaces of a Weyl semimetal and show that the corresponding confinement potential is similar to the application of a magnetic field. Among the numerous states, which can be labeled by indices n like in Landau levels, the $n=0$ surface state describes the Weyl semimetal Fermi arc at a given chemical potential. Moreover, the analogy with a magnetic field shows that an external in-plane magnetic field can be used to distort the Fermi arc and would explain some features of magnetotransport in Weyl semimetals. We derive the Fermi arc for type-I and type-II Weyl semimetals where we deal with the tilt anisotropy by the use of Lorentz boosts. In the case of type-II Weyl semimetals, this leads to many additional topologically trivial surface states at low energy. Finally, we extend the Aharonov-Casher argument and demonstrate the stability of the Fermi arc over fluctuations of the surface potential.