# Anomalous Hall transport in tilted multi-Weyl semimetals

## TL;DR

This paper investigates the anomalous Hall effect in tilted multi-Weyl semimetals under magnetic fields, revealing distinct behaviors between type-I and type-II phases and providing formulas for their conductivities.

## Contribution

It extends the understanding of Hall transport in multi-Weyl semimetals by deriving conductivity formulas for both type-I and type-II phases, including the effects of tilt and magnetic fields.

## Key findings

- Hall conductivity in type-I mWSMs generalizes from elementary Weyl semimetals.
- Vacuum Hall conductivity vanishes in type-II mWSMs at all temperatures.
- Thermal Hall and Nernst conductivities are characterized for both phases.

## Abstract

We study the effect of a perpendicular magnetic fieldBon a multinode Weyl semimetal (mWSM)of arbitrary integer monopole chargen, with the two Weyl multinodes separated ink-space. Besides type-I mWSMs, there exist type-II mWSMs which are characterized by the tilted minimal dispersion for low-energy excitations; the Weyl points in type-II mWSMs are still protected crossings but appear at the contact of the electron and hole pockets, after the Lifshitz transition. We find that the presence of a perpendicular magnetic field quantizes the occupation pockets due to the presence of Fermi tubes. In this theory, the Hilbert space is spanned by a set of $n$ chiral degenerate groundstates, and a countably infinite number of particle-hole symmetric Landau levels. We calculate the Hall conductivity for the tilt-symmetric case of type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and recover the well-known vacuum contribution. We compute the Fermi surface corrections and show that the expression generalizes from the formula for elementary ($n=1$) type-I WSMs. We derive an expression for the type-II mWSM Hall conductivity, which is bounded by a Landau level cutoff introduced on physical grounds. Interestingly, we find that the anomalous vacuum Hall conductivity is vanishing in the type-II phase at all temperatures. The corresponding thermal Hall and Nernst conductivities are evaluated and characterized for both phases. The qualitative and quantitative observations presented here may serve in the characterization of generic mWSMs of both types.