# Quantum Transport in Topological Semimetals under Magnetic Fields (II)

## TL;DR

This paper reviews recent advances in quantum transport phenomena in topological semimetals and insulators under varying magnetic field strengths, highlighting new mechanisms and theoretical insights into magnetoresistance, quantum oscillations, and Hall effects.

## Contribution

It introduces novel theoretical mechanisms for quantum Hall effects and Hall resistance reversal, expanding understanding of topological materials under strong magnetic fields.

## Key findings

- Negative magnetoresistance can occur without chiral anomaly.
- Proposed a new 3D quantum Hall effect mechanism via Weyl orbit tunneling.
- Observed Hall resistance reversal linked to Weyl fermion annihilation.

## Abstract

We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative magnetoresistance in topological semimetals and topological insulators by using the semiclassical equations of motion with the nontrivial Berry curvature. We show that the negative magnetoresistance can exist without the chiral anomaly. At strong magnetic fields, we establish theories for the quantum oscillations in topological Weyl, Dirac, and nodal-line semimetals. We propose a new mechanism of 3D quantum Hall effect, via the "wormhole" tunneling through the Weyl orbit formed by the Fermi arcs and Weyl nodes in topological semimetals. In the quantum limit at extremely strong magnetic fields, we find that an unexpected Hall resistance reversal can be understood in terms of the Weyl fermion annihilation. Additionally, in parallel magnetic fields, longitudinal resistance dips in the quantum limit can serve as signatures for topological insulators.