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

TL;DR

This paper models the Fermi arc in Weyl semimetals using a magnetic field analogy, revealing how surface states behave under magnetic distortions and surface potential fluctuations, with implications for magneto-transport.

Contribution

It introduces a magnetic field analogy for finite-sized Weyl semimetal interfaces and derives the Fermi arc for both type-I and type-II Weyl semimetals, including effects of tilt anisotropy.

Findings

Fermi arc states can be described by Landau level-like indices.

External magnetic fields can distort the Fermi arc, affecting magneto-transport.

Type-II Weyl semimetals exhibit additional trivial surface states at low energy.

Abstract

We consider finite-sized interfaces of a Weyl semi-metal 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 magneto-transport 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.