# Topologically distinct Weyl-fermion pairs: on the effect of magnetic tunnelling

## TL;DR

This paper explores how different topological configurations of Weyl-fermion pairs affect their electronic properties under magnetic fields, revealing that vorticity, not chirality, governs zero-energy modes and other phenomena.

## Contribution

It identifies the impact of Weyl node vorticity on Landau levels and topological features, distinguishing between different connection topologies of Weyl nodes.

## Key findings

- Zero-energy Landau levels are linked to vorticity, not chirality.
- Magnetic tunneling does not always remove zero-energy modes.
- Disorder effects and surface states vary with topological configuration.

## Abstract

A Weyl semimetal has Weyl nodes that always come in pairs with opposite chiralities. Notably, different ways of connection between nodes are possible and would lead to distinct topologies. Here we identify their differences in many respects from two proposed models with different vorticities. One prominent feature is the behaviour of zeroth Landau levels (LLs) under magnetic field. We demonstrate that the magnetic tunnelling does not always expel LLs from zero energy because the number of zero-energy modes is linked to the vorticity of the Weyl nodes, instead of the chirality. Other respects in disorder effects for weak (anti-)localization, surface Fermi arcs, and Weyl-node annihilation, are interesting consequences that await future exploration.