# Merging of momentum-space monopoles by controlling magnetic field: From cubic-Dirac to triple-Weyl fermion systems

## TL;DR

This paper studies how magnetic fields can merge monopoles in generalized Dirac systems, leading to multiple-Weyl semimetals with enhanced topological effects and multiple Fermi arcs, especially in cubic-Dirac and triple-Weyl fermions.

## Contribution

It introduces a generalized Dirac model with N-th power dispersion and shows how magnetic fields induce monopole merging into multiple-Weyl systems with enhanced topological phenomena.

## Key findings

- Monopole-antimonopole pairs emerge beyond a critical magnetic field.
- Monopoles merge into a single charge N when magnetic field aligns with z-axis.
- Multiple-Weyl semimetals exhibit N-fold enhanced anomalous Hall effect and Fermi arcs.

## Abstract

We analyze a generalized Dirac system, where the dispersion along the $k_{x}$ and $k_{y}$ axes is $N$-th power and linear along the $k_{z}$ axis. When we apply magnetic field, there emerge $N$ monopole-antimonopole pairs beyond a certain critical field in general. As the direction of the magnetic field is rotated toward the $z$ axis, monopoles move to the north pole while antimonopoles move to the south pole. When the magnetic field becomes parallel to the $z$ axis, they merge into one monopole or one antimonopole whose monopole charge is $\pm N$. The resultant system is a multiple-Weyl semimetal. Characteristic properties of such a system are that the anomalous Hall effect and the chiral anomaly are enhanced by $N$ times and that $N$ Fermi arcs appear. These phenomena will be observed experimentally in the cubic-Dirac and triple-Weyl fermion systems ($N=3$).