# Quantum Hall effect in three-dimensional graphene

## TL;DR

This paper theoretically investigates the quantum Hall effect in 3D graphene networks, revealing quantized Hall conductivity in special energy regions linked to chiral snake states and topological surface contours.

## Contribution

It uncovers the universal presence of chiral snake states and quantized Hall conductivity in 3D graphene, extending understanding beyond 2D systems.

## Key findings

- Quantized Hall conductivity occurs in specific energy regions.
- Chiral snake states travel along zero magnetic field contours.
- Quantization depends on the topology of the surface contour.

## Abstract

We theoretically study the electronic band structure and the Hall effect in the negatively-curved three-dimensional (3D) graphene network in magnetic fields. We found that special energy regions appear above and below the zero-energy Landau level, where the 3D Hall conductivity is quantized even though the spectrum is not fully gapped. The energy regions are dominated by the chiral snake states traveling along the zero magnetic field contour on the 3D surface, and the quantization of the Hall conductivity crucially depends on the topology of the contour. The exclusive energy region for the chiral states is found to be a universal feature of 3D graphene systems.