# Fate of Weyl semimetals in the presence of incommensurate potentials

## TL;DR

This paper studies how incommensurate potentials affect Weyl semimetals, showing robustness of Weyl points without Fermi arcs and vulnerability of Fermi arcs to weak potentials, with implications for ultracold atomic systems.

## Contribution

It reveals the differential impact of incommensurate potentials on Weyl semimetals with and without Fermi arcs, highlighting robustness and fragility aspects.

## Key findings

- Weyl points are robust against incommensurate potentials below a critical strength.
- Weyl semimetals with Fermi arcs are sensitive and can have arcs destroyed by weak potentials.
- A phase transition to a metallic state occurs when the potential exceeds a critical value.

## Abstract

We investigate the effect of the incommensurate potential on Weyl semimetal, which is proposed to be realized in ultracold atomic systems trapped in three-dimensional optical lattices. For the system without the Fermi arc, we find that the Weyl points are robust against the incommensurate potential and the system enters into a metallic phase only when the incommensurate potential strength exceeds a critical value. We unveil the trastition by analysing the properties of wave functions and the density of states as a function of the incommensurate potential strength. We also study the system with Fermi arcs and find the Fermi arcs are sensitive against the incommensurate potential and can be destoryed by a weak incommensurate potential.